Question

Taletha is preparing for an exam in Algebra II. She knows she will be expected to determine if two functions are inverses of each other using composition of functions. Which statement below correctly explains the relationship between two inverses, f and g, using composition of functions? Please help out

Answer 1

Option (4).

Explanation:

If a function is f(x) = 7x - 3

Inverse of the function will be,

g(x) =
`f^(-1)(x)` =
`(x+3)/(7)`

Now composite function f[g(x)] =
`7((x+3)/(7))-3`

= x

And g[f(x)] =
`((7x-3)+3)/(7)`

= x

Hence, condition for the inverse functions will be,

f[g(x)] = g[f(x)] = x

Therefore, Option (4) will describe the the composition of two functions.