Questions on Algebra: Functions, Domain, NOT graphing answered by real tutors!

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Question 947367: Problem: Determine whether the equation defines y as a function of x. Explain why or why not.
a.) x^2+y=9

b.) x+sqrt(y)=5
Click here to see answer by josgarithmetic(39618)

Question 947436: Beyond confused about interval notation.
Say I need to find the domain of: g(x)=√(x+7) - 1/x
So I know I need to set √(x+7)≥0 and then the denominator of -1/x is x>0.
Therefore, the answers would be:
x≥-7 and x>0 ok I understand this far. But interval notation keeps confusing me.
Why is the answer suppose to be -7≤x<0
I know that x≥-7 is the same as -7≤x because for x to be greater than -7 therefore -7 must be ≤x I understand that so -7≤x makes sense but where does the x<0 come from? How can x>0 be the same as x<0 for the answer, How is x greater than zero the same as x less than zero?
Please help
Click here to see answer by josgarithmetic(39618)

Question 947463: g(x)=2/x+1;x=0, x=h
Click here to see answer by Alan3354(69443)

Question 947497: are my domains correct?
√(x-5)^2: [5,inf)
√(x^2-5): [5,inf)
(√(25-x^2))/√(1+x): (-1,5]U[5,inf)
Thanks!
Click here to see answer by MathLover1(20850)

Question 947667:
(i) Find the domain of F. Write your answer in interval form
(ii) Find and ( ). Simply answers.

Please help
Click here to see answer by josgarithmetic(39618)

Question 947856: http://i.imgur.com/9uqTamL.png

How to figure out the vertices and properties of the ellipse?
Click here to see answer by Fombitz(32388)

Question 947948: for f(x)=3x^2+5 and g(x)=7x-2,
a)verify:g(x+2)not equal to g(x)+g(2).
b)find(f-g)(x).
c) using the resulting function in (b), show that (f-g)(2)=f(2)-g(2).
d)is (fg)(0)= (f/g)(0)?explain.
e)find f(x+h)-f(x)/h,h is not equal to 0

Click here to see answer by MathLover1(20850)

Question 947946: for each planet in a solar system, its year is the time it takes the planet to revolve around the center star.the formula E= 0.2X^3/2 models the number of the earth days in a planet's year,E, where x is the average distance of the planet from the center star,in millions of kilometers. there are approximately 88 Earth days in the year of the planet mercury.What is the average distance of mercury from the star? Round to the nearest million kilometers.clearly state your final answer in a complete sentence.
Click here to see answer by ankor@dixie-net.com(22740)

Question 948107: A parabola has the vertex (2, -30 ) and passes through the point (5, -12 ). Find a function f with this graph.
f(x) =
Please explain how I would find the solution
Thank you
Click here to see answer by stanbon(75887)

Question 948126: Have to complete the square for these:
Let f(x) = 2x^2 + 6x
please help!
Click here to see answer by josgarithmetic(39618)

Question 948126: Have to complete the square for these:
Let f(x) = 2x^2 + 6x
please help!
Click here to see answer by MathLover1(20850)

Question 948124: Express the quadratic function in standard form
f(x) = -x^2+4x
must find the vertex, x-intercept and y-intercept
Please help!

Click here to see answer by josgarithmetic(39618)

Question 948124: Express the quadratic function in standard form
f(x) = -x^2+4x
must find the vertex, x-intercept and y-intercept
Please help!

Click here to see answer by lwsshak3(11628)

Question 948148: The graph of a function F is a parabola that has the x-intercepts 9 and 21. The function has a minimum value of -54
Thanks
Click here to see answer by josgarithmetic(39618)

Question 948145: f(x) = −x^2 + 10x
Express the quadratic function in standard form.
Thanks
Click here to see answer by Fombitz(32388)

Question 948145: f(x) = −x^2 + 10x
Express the quadratic function in standard form.
Thanks
Click here to see answer by MathTherapy(10552)

Question 948285: Use f(x) = 7x − 2 and g(x) = 5 − x^2 to evaluate the expression

g(f(1))

Click here to see answer by MathLover1(20850)

Question 948282: Finding the vertex and x and y intercepts of: G(t)=1/2(t^2-4t)?
I know I can turn this into vertex form like so:
G(t)=1/2(t^2-4t+4)-4
G(t)=1/2(t-2)^2-4
so then the vertex would be
(2,-4) but graphing it online it states that the vertex is:(2,-2) what am I missing here? what makes it a -2 instead of a -4?
Please also explain how to find the x and y intercepts thank you
Click here to see answer by Fombitz(32388)

Question 948301: Someone please could help me with it?
Find the inverse function of f(x)= -2x + 4. Tell me if that function is one on one function.
Click here to see answer by ankor@dixie-net.com(22740)

Question 948314: Could someone help me with that.
Find the inverse of f(x)= x/x+4

Thanks.
Click here to see answer by harpazo(655)

Question 948333: given f(x)=2x^2+5x+3.
a) the y-intercept
b) the x-intercept, if any
c) the vertex
Click here to see answer by macston(5194)

Question 948337: Find the average rate of change, A, of g(x)=3/x from x=a to x=a+h. Simplify answer h should not be a denominate for final answer.
Thanks
Click here to see answer by harpazo(655)

Question 948380: Find the inverse function of f(x)= 4-x^2, x=> 0
Click here to see answer by amarjeeth123(569)

Question 948369: state the intervals where the function is increasing, decreasing, or constant.
The function is: f(x)=-1|x-2|+2
Click here to see answer by josgarithmetic(39618)

Question 948363: Let f(x) = √(x-4) - 1 and g(x) = (x+1)^2+2x. Find (g�f)(x) and simplify your answer. Final answer should not have any parentheses.
Is my answer correct?
(√(x-4) -1+1)^2 +2(√(x+4) - 1)
= x-4+2√(x-4) + 2
= x+2√(x-4) - 2
^
||
Is this the right answer?
THANKS
Click here to see answer by josgarithmetic(39618)

Question 948403: a. Find the domain of the function defined by Write your answer in interval form.
b. Find the average rate of change, A, of from to Don't forget to simplify your answer. (h should not be in the denominator answer)
Thank you
Click here to see answer by josgarithmetic(39618)

Question 948561: Change the subject of the following function to the symbol shown in brackets.The subject is [z].
3y = 4x + sqrt (3z � 4)
Click here to see answer by Fombitz(32388)

Question 948659: Please help me with the problem below :
Let c(x) = (4/(x+2)) - 2, find c^-1(x)
Click here to see answer by josgarithmetic(39618)

Question 948719: Write a function rule for each situation.
the area A(r) of a circle with radius r
Click here to see answer by amarjeeth123(569)

Question 948875: Identify the simplest form for the addition of the functions and
Click here to see answer by Fombitz(32388)

Question 948967: The minimum point on the graph of the equation is (-1,-3). What is the minimum point on the graph of the equation ?
1) (-1,2)
2) (-1,-8)
3) (4,-3)
4) (-6,-3)
Click here to see answer by Fombitz(32388)

Question 949183: Determine the expression for .

Click here to see answer by Fombitz(32388)

Question 949267: Is it possible for x=-2 to be in the Domains of the functions:
a.) R(x)= 3x^3 - 5x + 6 (all over) x + 2
b.)
Explain why or why not for each function. What are the Domains of the functions R(x) and H(x)? If required, use inf for the infinity sign.
Thank You for any help you can provide, I cannot find how to figure out these questions in my notes anywhere so if you can explain how you received each answer that would be great. Thank you again!

Click here to see answer by Theo(13342)

Question 949273: We are given two functions, and .
a) Is it true that for all values of x?
b) Is it true that for all values of x?

c) Is it true that ?
Click here to see answer by Fombitz(32388)

Question 949270: Given the functions and , find the indicated values.
a)

b)

Please explain how you figured out the answer, I appreciate any help you can provide. Thank you!
Click here to see answer by stanbon(75887)

Question 949327: let f(x)=4x-3 and g(x)=x^2-2x
find
(f/g)(x)
Click here to see answer by Theo(13342)

Question 949345: Someone help me with this please. I highly appreciated.
A function is given. Determine the average rate of change of the function between the given values of the variable.
f(x) = 5x^2; x = 4, x = 4 + h
Click here to see answer by Theo(13342)

Question 949547: Someone please help me with that.
Write the quadratic equation in the standard form. 6x^2-2x+9
Click here to see answer by MathLover1(20850)

Question 949715: Someone please help me with it.
-x^2-3x+3
Express the function as f(x)= a (x-h)^2 +k
Find the Y and X intercepts
Click here to see answer by josgarithmetic(39618)

Question 949710: how to change a quadratic equation to a vertex form
Click here to see answer by josgarithmetic(39618)

Question 949689: Given the functions, and , determine an expression for h(x) such that .
Having trouble with this practice question, please help.
Thank you
Click here to see answer by josgarithmetic(39618)

Question 949790: For (f+g) (x), do you just plug in the expressions for f(x)= and g(x)=
Click here to see answer by Alan3354(69443)

Question 949790: For (f+g) (x), do you just plug in the expressions for f(x)= and g(x)=
Click here to see answer by MathLover1(20850)

Question 949779: Determine the domain and range for (x+4)^2+(y+5)^2=25
Click here to see answer by josgarithmetic(39618)

Question 949840: If f(x)=x� and g(x)= 3x-4, find (g�f)(x)
Here;s what I am getting:
(g�f)(x) → g(f(x))
g(x�)

I am confused as to if the answer would be 3x�- 4x� or would I just simply substitute x� making the answer 3x�-4
Click here to see answer by jim_thompson5910(35256)

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