Question

If two functions are inverses of each other, which 2 statements are true?

Group of answer choices

A) f(g(x)) = x and g(f(x)) is equal to x

B) The graph of an inverse of a function is a reflection of the function across the line y=0.

C) The graph of an inverse of a function is a reflection of the function across the line y=x.

D) f(g(x)) = x and g(f(x)) is equal to 1

Answer 1

A and C

Explanation:

For 2 functions f(x) and g(x) to be inverses of each other, then

f(g(x)) = g(f(x)) = x → A

Given the graph of f(x) then the graph of it's inverse is obtained by reflecting the graph of f(x) in the line y = x → C

Answer 2

A and C

Explanation:

We are given that two functions are inverses of each other.

We have to find two statements are true about given functions.

Suppose f(x) and g(x) are two functions which are inverses to each other.

When f(x) and g(x) are inverses to each other then

A.
`f(g(x))=x` and
`g(f(x))=x`

Suppose f(x) =x+2 and g(x)=x-2

f(x) and g(x) are inverses to each other

`f(g(x))=f(x-2)=x-2+2=x`

`g(f(x))=g(x+2)=x+2-2=x`

Hence, option A is true.

`f(x)=x+2`

Suppose ,
`y=f(x)=x+2`

Replace x by y and y replace by x

`x=f(y)=y+2`

`y=x-2`

Replace y with
`f^(-1)(x)`

Then, we get
`f^(-1)(x)=x-2=g(x)`

Therefore, the graph of an inverse of a function is a reflection of the function across the lines y=x

Answer:A and C