Question

For f(x)= x+3 and g(x)= 3x+3, find the following functions

a:

(fog)(x)​

b.

(gof)(x)​

c.

(fog)(1)​

d.

(gof)(1)​

 

Answer 1

For f(x)= x+3 and g(x)= 3x+3, find the following functions

a)

(fog)(x)  =  f( g(x) )

              =  f(3x + 3)​

              =  (3x + 3)​ + 3

              =  3x + 6

b)

(gof)(x)​  =  g( f(x) )

              =  g(x + 3)

              =  3(x + 3) + 3

              =  3x + 9 + 3

              =  3x + 12

c)

(fog)(1)​

Substitute x = 1 in fog(x)

(fog)(1)  =  3(1) + 6

              =  3 + 6

              =  9

d)

(gof)(1)​

Substitute x = 1 in gof(x)

(gof)(1)​  =  3(1) + 12

              =  3 + 12

              =  15

Answer :

a)  (fog)(x)​  =  3x + 6

b)  (gof)(x)​  =  3x + 12

c)  (fog)(1)​  =  9

d)  (gof)(1)​  =  15.