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

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Question 828946: Find a linear function f(x) = mx + b such that m is positive and (f(f(x))= 9x + 4.
The answer is 3x + 1 and I can find this by trial and error. What I want to know is how to reach this answer mathematically.
I've tried to do it this way: 9x + 4 = m(mx + b) + b = m^2(x) + bm + b but then I got stuck because I have too many unknowns to solve by the quadratic equation.
Could you please explain this to me?
Thanks in advance
Click here to see answer by oscargut(2103)

Question 828994: Hi! I have been working on this problem for awhile. The answer key says the answer is -8, but I just don't understand. Thanks.
g(x) = x - 2x^2
g(-3) + 13
Click here to see answer by Fombitz(32388)

Question 829017: I need to solve for h(x) given that h(x) = (f◦g)^-1(x)
f(x) = and g(x) = x+4
Give a domain restriction if necessary.
Thank you for your time.
Click here to see answer by Edwin McCravy(20055)

Question 829491: Please help me solve this equation: sqrt(9x-5)=3x^2+2x+3
Click here to see answer by Fombitz(32388)

Question 829491: Please help me solve this equation: sqrt(9x-5)=3x^2+2x+3
Click here to see answer by Edwin McCravy(20055)

Question 829651: what is the range of the function f(x)=9x-1
Click here to see answer by LinnW(1048)

Question 829754: Suppose you are driving on a straight road at 35 mph how far have you traveled after 2 hours
Click here to see answer by Alan3354(69443)

Question 829779: what is the range of f(x)=x^2-4
Click here to see answer by reviewermath(1029)

Question 829737: At Market A , 1-lb packages of rice are sold for $2. At Market B rice is sold in bulk for $2/lb. For each Market write a function describing the cost of buying rice in terms of the weight. How are domains of the 2 functions different?
Click here to see answer by josgarithmetic(39617)

Question 829966: I need help figuring out how to find the domain and range of a function in vertex form. For example y= 1.75(x+3)^2+3
Click here to see answer by LinnW(1048)

Question 829966: I need help figuring out how to find the domain and range of a function in vertex form. For example y= 1.75(x+3)^2+3
Click here to see answer by TimothyLamb(4379)

Question 830317: Let f(x) = -2x - 7 and g(x) = -4x + 6. Find (fog)(-5)
Click here to see answer by Fombitz(32388)

Question 830346: What is the domain of the function h(x)=8x/(x(x^2-81))?
Click here to see answer by math-vortex(648)

Question 830347: F(x)=x^2+7 and g(x)= x+3/x find (g o f)(-5)
Click here to see answer by LinnW(1048)

Question 830767: How do you solve a function with a power? for example:
f(x)=(x+3) to the 3/2 power?
the (x+3) also has a squared root above it.

Click here to see answer by MathLover1(20849)

Question 829717: Find domain of f(x)=√5x-12
Click here to see answer by Fombitz(32388)

Question 830977: find the average rate of change of f(x)=x^2+6:
a. from 1 to 3
b. from 2 to 4
c. from -2 to 1
Click here to see answer by Alan3354(69443)

Question 831047: Azim is the best basketball playerof all time.The height of his basketball shot from the top of his head is modeled by the function h(t)=-t^2+4t+6, h(t) us vertical displacement from his head and t is is time in seconds. Azim is 6 feet tall and standing on the ground. What is the maximum height in feet that the ball will reach from the ground?
Click here to see answer by nerdybill(7384)

Question 831343: A function is given. Determine the average rate of change of the function between the given values of the variable.
f(x) = 3x^2; x = 4, x = 4 + h

Click here to see answer by stanbon(75887)

Question 831341: A function is given. Determine the average rate of change of the function between the given values of the variable.
f(x) = 3x2; x = 4, x = 4 + h

Click here to see answer by stanbon(75887)

Question 831331: Construct two composite functions

(g � f) (x)=
(g � f) (2)=
(f � g) (x)=
(f � g) (2)=

Click here to see answer by stanbon(75887)

Question 831350: A function is given below. Determine the average rate of change of the function between the given values of the variable.
g(x) = 2/x

x = 5, x = a

Click here to see answer by Fombitz(32388)

Question 831344: A function is given below. Determine the average rate of change of the function between the given values of the variable.
g(x) = 2/x
x = 5, x = a

Click here to see answer by Fombitz(32388)

Question 830971: find the domain of the function h(x)=x-4/x^3-9x
Click here to see answer by Fombitz(32388)

Question 831221: find the value of c so that the natural domain of the following function is (-∞,3)U (3,∞)
f(x)=1/x+4c
Click here to see answer by Fombitz(32388)

Question 831474: 17. f(x) = -14x2 - 14x + 11
g(x) = -14x2 + 14x + 12
find g(f(3))
A. 356785
B. -356786
C. 3456345
D.-342553
E. -347272
F. -324564
Click here to see answer by hovuquocan1997(83)

Question 831970: Is the function y=x/3+2 linear. I'm not sure.
Click here to see answer by jim_thompson5910(35256)

Question 832193: If the domain of f(x) is given by [-1,5], what is the domain of |f(x)|?
Click here to see answer by Fombitz(32388)

Question 832249: Let f(x)=4x^2-x and g(x)=2^2
F(x) + g(x)
How to solve this ?

Click here to see answer by Fombitz(32388)

Question 832359: Given, f(x+2)=x^2+3. Then solve it, f(x+4)=?
Click here to see answer by Fombitz(32388)

Question 832368: If f (x)= x+6 and g (x)= x^4 what is g (f(x))
Click here to see answer by stanbon(75887)

Question 832390: 1. g(x) = x2 - 8, f(x) = (-x + 1)^1/2

A. (-x2 + 9)^(1/2)
B. (-x2 - 8)^(1/2)
C. (-x + 1)^(1/2) (x2 - 8)
D. (-x + 1)^(1/2) (x2 - 8)
E. (-x2 - 9)^(1/2)
F. (x - 2)^2

2. g(x) = (x2 -16)^(1/2), f(x) = (3 - x)^(1/2)

A. (3 - x)^(1/2), (x2 -16)^(1/2)
B. (-x-13)^(1/2)
C. (3-(x2 -16)^(1/4))
D. (3x2 + 16)
E. (3x(1/2) + 16)
F. (3-(x2 -16)^(1/2))^(1/2)
Click here to see answer by Fombitz(32388)

Question 832627: What is the value of f(-9) when f(x)=2x to the power of 2 +3x-4
Click here to see answer by math-vortex(648)

Question 832713: 1.3 What is f o g if:
f(x) = -2x+7 and g(x)=x+2
Thank you for your assistance, I am rather lost on this problem.
Click here to see answer by oscargut(2103)

Question 833092: If f(x) = 9 − 2|x + 2|, find f(−7)
Click here to see answer by Fombitz(32388)

Question 832922: When asked whether the relation
{(-4,16), (-2,4), (0,0), (2,4)} is a function, a student stated that the relation is not a function because 4 appears twice. What error did the student make? How would u explain to the student why this relation is not a function.
Click here to see answer by Fombitz(32388)

Question 832633: Area= 32x+40 what can the length and width be equal to? And how do you get it
Click here to see answer by Fombitz(32388)

Question 833415: Find the domain of the function.
(a) (2x+1)/(x^2+x-2)
(b) cube square of x/x^2+1
(c)(sqrt4-x)+(sqrtx^2 -1)

Click here to see answer by stanbon(75887)

Question 833483: I'm in need of help very badly I have read and reread the assignment looked at the example.And I still don't understand I talked to my professor done what she said to do and nope it's a lost cause i'm starting to think , I have used tutors
but we are only allowed so many hours. here's the question.
6
--
7
+
3 3
--
7
------
Click here to see answer by Alan3354(69443)

Question 833479: For what real numbers x does the expression represent a real number?

√(x_9)
Click here to see answer by Alan3354(69443)

Question 833502: I"m stuck here 4 2/3 - 3 3/5
Click here to see answer by checkley79(3341)

Question 833533: I 'm stuck on this part 19 3/4 - 9 9/10 =
Click here to see answer by stanbon(75887)

Question 833581: Hello i'm stuck here and have been trying to get it but no luck it's
21 5/9 -7 11/15
Click here to see answer by JulietG(1812)

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