Question

F(x)=

2

x

2

−

5

x

−

8

2x

2

−5x−8

g

(

x

)

=

g(x)=

 

 

−

5

x

+

4

−5x+4

Find:

(

g

∘

f

)

(

x

)

Find: (g∘f)(x)

Answer 1

`(g\ o\ f)(x) = -10x^2 + 25x + 44`

Explanation:

Given

`f(x) = 2x^2 - 5x - 8`

`g(x) = -5x+4`

Required

`Find:\ (g\ o\ f)(x)`

In functions;

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

Substitute
`f(x) = 2x^2 - 5x - 8` in
`(g\ o\ f)(x) = g(f(x))`

`(g\ o\ f)(x) = g(f(2x^2 - 5x - 8))`

Solving for
`g(f(2x^2 - 5x - 8))`

If
`g(x) = -5x+4`

then

`g(f(2x^2 - 5x - 8)) = -5(2x^2 - 5x - 8) + 4`

Open Bracket

`g(f(2x^2 - 5x - 8)) = -10x^2 + 25x + 40 + 4`

`g(f(2x^2 - 5x - 8)) = -10x^2 + 25x + 44`

Recall that:

`(g\ o\ f)(x) = g(f(2x^2 - 5x - 8))`

This implies that

`(g\ o\ f)(x) = -10x^2 + 25x + 44`