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

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 Algebra: Functions, Domain, NOT graphing Solvers Lessons Answers archive Quiz In Depth

 Question 45202: Find the maximum or minimum value of the function: f(x) = 1 + 3x -x^2 = x^2 + 3x + 1 =-(x^2 -3x + 2.25) +1 + 2.25 =-(x^2 -3x + 2.25) + 3.25 x= -b/2a = -3/2(-1) = 3/2 = max 1.5 y = 3.25 Thank you so much! Click here to see answer by rapaljer(4667)

 Question 45205: Find the maximum or minimum value of the function f(x) = -x^2/3 + 2x + 7 x = 2/2(-1/3) = 2/(-2/3)= (2/1)(3/2)= 3 maximum (-x^2 + 6x + 21 /3) = ((-x^2 + 6x + 9) + 21 + 9)/3) = (-(x + 3)^2 + 30)/3 = -(x + 3)^2 + 10 y = 10 Thanks so much! Click here to see answer by rapaljer(4667)

 Question 45311: Use g(x)= 2 - x^2 to evaluate the expression g(g(3)) 2-(2-3^2)^2 = 2 - (11)^2 = 119 Thank you for all your wonderful assistance! Click here to see answer by tutmath(14)

 Question 45309: Find the domain of the function g(x) = sqrt(x+1) - (1/x) domain [-1, infinity) u [-1, infinity) = [-1, infinity) x not equal to 0 Thanks for all your help! Click here to see answer by Nate(3500)

 Question 45369: It's been 15 years since I've taken algebra, please show me how you got to the answer. If f(4)=0 and f(6)=6, what could represent f(x)?x can represent anyone number that solves the equation Click here to see answer by hope(1)

 Question 45484: f(x) = x2 -7x + 10 Find (a) f(0),(b) F(5), and (c)f(-2) Click here to see answer by Nate(3500)

 Question 45520: Use the property of Inverse Functions to show that f and g are inverses of each other: f(x) = x^3 + 1; g(x) = (x-1)^(1/3) f(g(x)) = f((x-1)^1/3) + 1 = x-1 + 1 = x g(f(x)) = g(x^3 + 1) = (x^3 + 1)^3 + 1 = x + 1 -1 = x f and g are inverses of each other. Thank you very much! Click here to see answer by stanbon(57407)

 Question 45524: Find the inverse function of f f(x) = sqrt(2x-1) y=sqrt(2x-1) y^2 = 2x-1 y^2 + 1 = 2x (y^2 +1)/2 = x f^-1(x) = y^2 + 1/2 Thank you so very much! Click here to see answer by stanbon(57407)

 Question 45521: Find the inverse function of f f(x) = x-2/x+2 y = x-2/x+2 = (x+2)y = x-2 yx + 2y = x-2 yx-x = -2y-2 x(y-1) = -2y-2 x = 2(y-1)/y-1 f^-1(x) = 2x-2/y-1 Thank you for all your help! Click here to see answer by stanbon(57407)

 Question 45518: Use the Property of Inverse Functions to show that f and g are inverses of each other: f(x) = 2x, g(x) = x/2 f(g(x)) = f(x/2) = 2(x/2) = x g(f(x)) = g(2x) = 2(x/2) = x f and g are inverses of each other, correct? Thank you very much! Click here to see answer by stanbon(57407)

 Question 45485: rewrite as an equation as a function of x -3x + 4y = 11 Click here to see answer by adamchapman(301)

 Question 45583: A company produces a product for which the variable cost is \$10.20 per unit and the fixed cost is \$13000.The product sells for \$ 19.99.Let x be the number of unitsproduced and sold. a)Write the total cost of C as a function of the number of units produced. b)Write the revenue R as a function of the number of units sold c)Write the profit P as a function of the number of units sold. Click here to see answer by stanbon(57407)

 Question 45654: I told my grandson I would help with his homework and I don't have the heart to tell him I don't know it Could you answer these questions for me: Why is function notation important? and what's the reasons for function notation? I have not the slightest idea, can you help me on this one? Bless you heart.....Bessie Click here to see answer by stanbon(57407)

 Question 45660: If f(x) = 5x  1 find following f(a-2) Click here to see answer by AnlytcPhil(1278)

 Question 45752: Find the equation of the following line, write the equation in the slope intercept form. Identify the slope and y-intercept. Through (1,4) and parallel to x  2y = 6 Click here to see answer by tutmath(14)

 Question 45756: True or False. Explain The expression17+4(y-6) is read as the sum of 17 and the difference of y and 6 times 4. Click here to see answer by stanbon(57407)

 Question 45790: From a square piece of cardboard with width x inches, a square of width x-3 inches is removed from the center. Write the area of the remaining piece as a function of x. I am at a loss on how to start solving this one. Click here to see answer by checkley71(8403)

 Question 45758: Formulate and solve an equation(s) for the following statement to find the value of the integers. Four consecutive odd integers have a sum of 120. What are the integers? Click here to see answer by checkley71(8403)

 Question 45750: (7) Write the equation of the line passing through (-3,1) with a slope of-1/3 Write the equation in the slope intercept form and in standard form. Click here to see answer by checkley71(8403)

 Question 45850: the following two lines represent a function: line (1) has points a(-3,1) b(-1,4) line (2) has points c(1,3) and d(4,1). Give the domain of the function. i know from my reading it says the Domain is the highest values that make the function work. but i am not sure what that means given the data above. Click here to see answer by tutorcecilia(2152)

 Question 45851: values of two functions (f) and (g) are listed below find the composite (f little circle g)(6). values for (f) [x=4 f(x)=7 ] for [x=5 f(x)=6] [for x=6 f(x)=5] [x=7 f(x)=4] values for (g) [x=4 g(x)=6 ] for [x=5 g(x)=7] [for x=6 g(x)=4] [x=7 g(x)=5] i know from my reading that the composite = f(g(x)) so does that mean i just go to the list and find what g(6)= which is 4. to find my answer. is it that simple. Click here to see answer by stanbon(57407)

 Question 45907: If P(4,-5) is a point on the graph of the function y=f(x), find the corresponding point on the graph of y=2f(x-6). Click here to see answer by stanbon(57407)

 Question 45753: Formulate and solve an equation(s) for the following statement to find the value of the integers. Four consecutive odd integers have a sum of 120. What are the integers? Click here to see answer by checkley71(8403)

 Question 45881: How do I even apprehend this? Can you explain each step for me please. Thanks. If the inventor charges \$4 per unit, then her profit for producing and selling x units is given by the function P(x)=2.25x-7000 (a) What is her profit if she sells 2000 units? (b) What is her profit if she sells 5000 units? (c) What is the break-even point for sales? Click here to see answer by Earlsdon(6287)

 Question 46049: Find h(g(f(-46))) if f(x) = x-8/9, g(x) =3 -x^2 and h(x)=[x-9] Click here to see answer by venugopalramana(3286)

 Question 46047: Find the quotient and remainder when : x^4-2x2+5x-4 is divided by x+3. Use either long or sythetic division Click here to see answer by venugopalramana(3286)

 Question 46074: For the function defined by f(x)=5x-4, find a formula for f^[-1(x)]. Thank you. Click here to see answer by Nate(3500)

 Question 46285: Without graphing, determine whether the system has one solution, no solution, or an infinite number of solutions. x+3y = 6 y = - 1/3x + 2 Click here to see answer by jake_6233(74)

 Question 46284: without graphing, determine whether the system has one solution, no solution, or an infinite number of solutions. x = -y y+ y = 2 thanks a bunch Click here to see answer by jake_6233(74)

 Question 46289: Suppose that x represents one of two positive numbers whose sum is 30. Determine a function f(x) that represents the product of these two numbers. Click here to see answer by jake_6233(74)
 Question 46289: Suppose that x represents one of two positive numbers whose sum is 30. Determine a function f(x) that represents the product of these two numbers. Click here to see answer by Earlsdon(6287)

 Question 46286: ok so without doing any graphing, we need to determine whether the system has 1, no, or infinite solutions. x + 2y = 6 y = - 1/2x + 3 thanks a bunch Click here to see answer by Earlsdon(6287)

 Question 46288: Question is: Give the domain of square root of x + 1 over x in interval notation. My first answer was (-infinity, 0) U (0, infinity). I got the second part right but I did not get the first part of the answer right. I know that the reciprocal function f(x) = 1/x contains the domains of (-infinity, 0)U (0, infinity) but apparently this does not help me. Can anyone help? Click here to see answer by AnlytcPhil(1278)

 Question 46562: Factor out the variable that is raised to the smaller exponent Click here to see answer by josmiceli(9697)

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