Question

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

Answer 1

ANSWER

The correct answer is C

EXPLANATION

If two f(x) and g(x) are inverses of each other, then f(g(x))= g(f(x))=x.

for option A,

$f(g(x)) = 2 + \sqrt[3]{2 - {x}^{3} }$

for option B,

$f(g(x)) = \frac{6x - 8}{6} + 8 = \frac{6x - 40}{6} = \frac{3x - 20}{3}$

for option C

$f(g(x)) = 5( \frac{x + 11}{5} ) - 11 = x + 11 - 11 = x$

for option D

$f(g(x)) = \frac{7}{ \frac{x + 9}{7} } - 9 = \frac{49 - 9(x + 9)}{x + 9} = \frac{ - 32 - 9x}{x + 9}$

The correct choice is C

Answer 2

Answer:

Option C.

Step-by-step explanation:

To know if two functions are inverse of each other we need to Plug the first function f (x) into the second one g (x) and simplify.  If g[f(x)]=x then f(x) and g(x) are inverses if not, they are not inverses.

The correct option is the C, given that:

f(x) = 5x - 11 and g(x) = (x+11) / 5

Pluggin f(x) into g(x)

g[f(x)]= (5x - 11 + 11)/5 = 5x/5 = x