Question

There are 3 unknown functions, f(x), g(x), and j(x). Give the following compositions between the functions. Which of the functions are inverses?

f(g(x)) = 2x - 3
f(j(x)) = 2x+5
g(f(x)) = 2x-1
g(j(x)) = x
j(f(x)) = 2x + 3
j(g(x)) = x​

Answer 1

g(x) and j(x)

Explanation:

You want to know which functions are inverses, given ...

• f(g(x)) = 2x - 3
• f(j(x)) = 2x+5
• g(f(x)) = 2x-1
• g(j(x)) = x
• j(f(x)) = 2x + 3
• j(g(x)) = x​

Inverse functions

Functions are inverses of one another if all (input, output) pairs of one of them exactly match all (output, input) pairs of the other one. That is, their composition is the identity function.

g(j(x)) = x and j(g(x)) = x indicate that g(x) and j(x) are inverse functions.

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