Question

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

Answer 1

Answer: A

Step-by-step explanation: A P E X

Answer 2

Answer:

Proved!

Step-by-step 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) = ∛$\frac{x - 10}{7}$

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

We get; 7($\frac{x - 10}{7}$) + 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!)