Question

A function is given:

f(x) = 3x + 12

a. Determine the inverse of this function and name it g(x).
b. Use composite functions to show that these functions are inverses.
c. Evaluate f(g(–2)). Explain: What is the domain?

Answer 1

I need help with a, b, and c please!

Answer 2

a. To find the inverse of a function do this:
Write the function as y = 3x + 12
Then swap x and y
Then solve for y
That function is the inverse of f(x) which you will call g(x)

Answer 3

(x-12)/3?

Answer 4

Correct.

Answer 5

Okay, now how to do b?

Answer 6

A function maps one number of its domain to one number in its range. In your case, for example, f(x) = 3x + 12, if you evaluate the function at x = 1, you get
f(1) = 3(1) + 12 = 15, so
f(1) = 15.
The function maps 1 to 15. If you give the function an input of 1, you get an output of 15.

The inverse function takes the value 15 and maps it back to 1.
g(x) = (x - 12)/3, so
g(15) = (15 -12)/3 = 3/3 = 1.

When you evaluate a function at an x value you get a certain y value. If you then evaluate the inverse function at that y value you get back to the original x value.

The composition of two functions is to evaluate one function at a certain value, the input, and get the output, and then feed that output as the input of the other function.

Answer 7

Since a function and its inverse do opposite mappings, if you do the composition of a function and its inverse, and evaluate it at any input the final result will be the same as the original input because you applied and "unapplied" the mapping.

Answer 8

Oh, okay, I got b down now c?

Answer 9

If you can show that fog(x) = x, then you have shown that the functions are inverses.

Answer 10

fog?

Answer 11

And so for b, I can just show your examples, and that should cover the answer for that?

Answer 12

Composition of function f and function g. fog(x) = f(g(x))
f(x) = 3x + 12
g(x) = (x - 12)/3