Question

Find the requested function value.

Find (f ∘ g)(-9) when f(x) = 9x + 5 and g(x) = -4x2 - 6x + 3.


A.-2398

B.-22,645

C.763

D.842

Answer 1

Given:

Given that the functions
`f(x)=9 x+5` and
`g(x)=-4x^2-6x+3`

We need to determine the value of the function
`(f \circ g)(-9)`

First, we shall determine the value of the function
`(f \circ g)(x)`

The value of the function
`(f \circ g)(x)`:

Let us determine the value of the function
`(f \circ g)(x)`

Thus, we have;

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

`=f(-4x^2-6x+3)`

`=9(-4x^2-6x+3)+5`

`=-36x^2-54x+27+5`

`(f \circ g)(x)=-36x^2-54x+32`

Thus, the value of the function is
`(f \circ g)(x)=-36x^2-54x+32`

The value of the function
`(f \circ g)(-9)`:

The value of the function
`(f \circ g)(-9)` can be determined by substituting x = -9 in the function
`(f \circ g)(x)=-36x^2-54x+32`

Thus, we have;

`(f \circ g)(-9)=-36(-9)^2-54(-9)+32`

`=-36(81)-54(-9)+32`

`=-2916+486+32`

`(f \circ g)(-9)=-2398`

Thus, the value of the function
`(f \circ g)(-9)` is -2398

Hence, Option A is the correct answer.