Question

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

Answer 1

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)) = (6x - 8)/(6) + 8 = (6x - 40)/(6) = (3x - 20)/(3)`

for option C

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

for option D

`f(g(x)) = (7)/( (x + 9)/(7) ) - 9 = (49 - 9(x + 9))/(x + 9) = ( - 32 - 9x)/(x + 9)`

The correct choice is C

Answer 2

Option C.

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