Question

Which of the following pairs of functions are inverses of each other?

Answer 1

Proved!

Explanation:

For two functions f(x) and g(x) to be inverses of each other then;

f(g(x)) = x and g(f(x)) = x condition must be satisfied.

Checking: A. f(x) = 7x³ + 10 and g(x) = ∛
`(x - 10)/(7)`

So f(g(x)) = 7(
`\sqrt[3]{(x- 10)/7}`)³ + 10

We get; 7(
`(x - 10)/(7)`) + 10 = x - 10 + 10 = x (*This is correct!)

So g(f(x)) =
`\sqrt[3]{((7x^3 + 10) - 10)/7}`

Ten cancels out and we are left with;

`\sqrt[3]{7x^3/7}` =
`\sqrt[3]{x^3}` = x (* This is also correct!)

Answer 2

Answer: A

Step-by-step explanation: A P E X