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

See explanations below

Explanation:

Given the function

f(x) = 3x+12

Let y = f(x)

y = 3x+12

Replace y with x

x = 3y+12

Make y the subject

3y = x-12

y = (x-12)/3

Hence the required inverse is!

g(x) = (x-12)/3

b) To show that the functions are inverses, we must show that f(g(x)) = g(f(x))

f(g(x)) = f((x-12)/3)

Replace x in f(x) with x-12/3

f(g(x)) = 3(x-12)/3 +12

f(g(x)) = x-12+12

f(g(x)) = x

Similarly for g(f(x))

g(f(x)) = g(3x+12)

g(f(x)) = (3x+12-12)/3

g(f(x)) = 3x/3

g(f(x)) = x

Since f(g(x)) = g(f(x)) = x, hence they are inverses of each other

c) Given f(g(x)) = x

f(g(–2)) = -2

The domain is the input variable of the function. Hence the domain is -2