Question

If f(x) = 4x + 3 and g(x) = √x-9 ,

which statement is true?

A.) 2 is in the domain of f ° g
B.) 2 is NOT in the domain of f ° g

Answer 1

Answer: Option B

2 is NOT in the domain of f ° g

Explanation:

First we must perform the composition of both functions:

If
`g(x) = √(x-9)` and not
`√(x) -9`

`f (x) = 4x + 3\\\\g (x) = √(x-9)\\\\f (g (x)) = 4 (√(x-9)) + 3`

The domain of the composite function will be all real numbers for which the term that is inside the root is greater than zero. When x equals 2, the expression within the root is less than zero

`f (g (x)) = 4 (√(2-9)) + 3\\\\f (g (x)) = 4 (√(-7)) + 3`

The root of -7 does not exist in real numbers, therefore 2 does not belong to the domain of f ° g

The answer is Option B.

Note. If
`g(x) = √(x)-9`

So

`f(g(x)) = 4(√(x))-36 + 3` And 2 belongs to the domain of the function