Question

If f (x) = x + 7 and g (x) = StartFraction 1 Over x minus 13 EndFraction, what is the domain of (f circle g) (x)?

StartSet x vertical line x not-equals 6 EndSet
StartSet x vertical line x not-equals negative 6 EndSet
StartSet x vertical line x not-equals negative 13 EndSet
StartSet x vertical line x not-equals 13 EndSet

Answer 1

d

Explanation:

Answer 2

Given that,

`f(x)=x+7\\\\g(x)=(1)/(x-13)`

To find,

`(f\circ g)(x)`

Solution,

We know that,

`(f\circ g)(x)=f(g(x))\\\\=f((1)/(x-13))\\\\=(1)/(x-13)+7\\\\=(7x-90)/(x-13)`

Domain is the set of input value. For the above function, if we put x = 13, then it will become undefined.

Domain = {x I x ≠ 13}

Hence, the correct option is (D) "StartSet x vertical line x not-equals 13 EndSet".