Given the functions fx4x7gx102xhxx2x2 find a f o g x b f o f

Given the functions; f(x)=4x+7,g(x)=10-2x,h(x)=x^2+x-2

find;

a) (f o g) (x)=

b) (f o f) (x)=

c) (f o h) (1)=

d) (g o g) (0)=

e) (g o f ) (-1)=

Solution

f(x)=4x+7,g(x)=10-2x,h(x)=x^2+x-2

a) (f o g) (x)=f(g(x))

=4(10-2x)+7

=40-80x +7

=47-80x

b) (f o f) (x)=f(f(x))

=4(4x+7) +7

=16x +28 +7

=16x +35

c) (f o h) (x)=f(h(x))

=4(x^2+x-2) +7

(f o h) (1)

=4(1^2+1-2) +7

=7

d) (g o g) (x)=g(g(x))

=10-2(10-2x)

(g o g) (0)

=10-2(10-2*0)

=10-20

=-10

e) (g o f ) (x)= g(f(x))

=10-2(4x+7)

=10-8x -14

=-4-8x

(g o f ) (-1)

=-4-8(-1)

=-4+8

=4