find the following functions.

Question

For f(x)=x+2 and g(x)=5x+2, find the following functions.

a. (g o f)(x)

b. (g o f)(-1)

Answer 1

The functions are f(x)=x+2 and g(x)=5x+2

1)

(g o f)(x)  =  g ( f(x) )

                =  g ( x + 2 )

                =  5( x + 2 )  + 2

                =  5x + 10 + 2

(g o f)(x)   =  5x + 12

2)

Substitute x = -1 in above composite function

(g o f)(-1)   =  5(-1)+ 12

(g o f)(-1)   = -5 + 12

(g o f)(-1)   = 7.

Answer :

1)  (g o f)(x)   =  5x + 12

2)  (g o f)(-1)   = 7.