Question

Let
`h(x) = (g` °
`f)(x) = \sqrt[]{x+3}`

Which of the following could be a possible decomposition of h(x)?

Answer 1

Choice D is correct answer.

Explanation:

We have given composition of two functions.

h(x) = (gof)(x) = √x+3

We have to find the two functions whose composition is given.

The formula to find the composition of functions:

(gof)(x) = g(f(x)

Choose f(x) = x+3

(gof)(x) = g(x+3)

Choose g(x) = √x

(gof)(x) = √x+3

Hence, answer is f(x) = x+3 and g(x) =√x

Answer 2

D.
`f(x)= x+3` and
`g(x)=√(x)`

Explanation:

We are given that,

Composition of two functions f and g is given by,

`h(x) = (g\circ f)(x) = √(x+3)`.

According to the options:

A.
`h(x) = (g\circ f)(x) = g(3x)=√(3x)`

B.
`h(x) = (g\circ f)(x) = g(x)=x+3`

C.
`h(x) = (g\circ f)(x) = g(√(x))=√(x)+3`

D.
`h(x) = (g\circ f)(x) = g(x+3)=√(x+3)`

Thus, we see that, option D is correct.

Hence,
`f(x)= x+3` and
`g(x)=√(x)` is a possible decomposition of h(x).