Need Algebra help?

Question

I have a few questions here, if anyone could provide answers, I would really appreciate it. I have already been through my book time and time again, I don't understand this crap. I've failed the class one and don't want to fail it again. I really need quick help here.... I'm beyond the "hints" stage at this point.

1) I have a graph. The x values are -5, -3 and 1. I need to find the y values for the inverse function f^-1

2) Given f(x) = x/2 find f^-1(4)

3) Given f(x) = 8x^3 and g(x) = 2x find each of the following

(f*g)(x)

(f/g)(x)

4) Given f(x) = 6x and g(x) = -2x, find each of the following

(f+g)(x)

(f-g)(1)

Answer 1

If I understand your question correctly, I think this is what you are looking for.

For the inverse function, get the value of the function and inverse it's value.

1. Identify the equation of the line on your graph and calculate the function values. Then get the inverse of these values.


2. f(x) = x/2
f(x) = 4/2
f(x) = 2
f^-1(x) = 1/2

3.
(f*g)(x) = f(x)*g(x) = (8x^3)*(2x) = 16x^4
(f/g)(x) = f(x)/g(x) = (8x^3)/(2x) = 4x^2

4.
(f+g)(x) = f(x)+g(x) = 6x+(-2x) = 4x
(f-g)(x) = f(x)-g(x) = 6x-(-2x) = 6x+2x) = 8x
(f-g)(1) = 4

Answer 2

1. The y values of any inverse function are the same as the x values of the non-inverse function. If I'm understanding the question correctly.
y values of inverse = -5, -3, 1.


2. f(x) = x/2
Solve the inverse
x = y/2
y = 2x
f^-1(x) = 2x
f^-1(4) = 2(4) = 8

3.
(f*g)(x) = f(x)*g(x) = (8x^3)*(2x) = 16x^4
(f/g)(x) = f(x)/g(x) = (8x^3)/(2x) = 4x^2

4.
(f+g)(x) = f(x)+g(x) = 6x+(-2x) = 4x
(f-g)(x) = f(x)-g(x) = 6x-(-2x) = 6x+2x) = 8x
(f-g)(1) = 8

Answer 3

Srry im only in da 5th form