Question

If f(x) = squareroot x + 5 and g(x) = -4x + 4,

which statement is true?
Click on the correct answer.
3 is in the domain of fºg.
3 is not in the domain of fºg.

Answer 1

3 is not in the domain of
`f\circ g`.

Explanation:

The given functions are

`f(x)=√(x+5)`

`g(x)=-4x+4`

We need to check whether 3 is in the domain of
`f\circ g` or not.

`f\circ g=f(g(x))`

`f\circ g=f(-4x+4)`
`[\because g(x)=-4x+4]`

`f\circ g=√((-4x+4)+5)`
`[\because f(x)=√(x+5)]`

`f\circ g=√(-4x+9)`

This function is defined if

`-4x+9\geq 0`

`9\geq 4x`

`(9)/(4)\geq x`

It means domain of the function
`f\circ g` is
`(-\infty,(9)/(4)]`.

`3\\otin (-\infty,(9)/(4)]`

Therefore, 3 is not in the domain of
`f\circ g`.