Question

Let f(x) = -2x - 7 and g(x) = -4x + 6. Find (gof)(-5).

Answer 1

`(gof)(-5)=-6`

Explanation:

One is given the following information;

`f(x)=-2x-7\\g(x)=-4x+6`

One is asked to find the following,

`(g o f)(-5)`

The expression (
`gof`) is another way to denote (
`g(f(x))`), in essence, substitute function (f) into function (g) in place of parameter (x). The simplify to find the resulting function;

`g(f(x))\\=-4(-2x-7)+6\\=(-4)(-2x)+(-4)(-7)+6\\=8x+28+6\\=8x+34`

One is asked to evaluate the function (
`gof`) for (-5). Substitute (-5) into the function and simplify to evaluate;

`(gof)(-5)=8x+34\\=8(-5)+34\\=-40+34\\=-6`

Answer 2

(g ￮ f )(- 5) = - 6

Explanation:

Evaluate f(- 5), then substitute the value obtained into g(x)

f(- 5) = - 2(- 5) - 7 = 10 - 7 = 3 , then

g(3) = - 4(3) + 6 = - 12 + 6 = - 6