Question

Let f(x) = x2 and g(x) = x + 5. Write an expression that represents each composition:

a. g(f(4))
b. f(g(4))
c. (f ∘ g)(x)

Answer 1

(a) 21

(b) 81

(c)
`(fog)x=(x+5)^2=x^2+10x+25`

Explanation:

We have given the function
`f(x)=x^2\ and g(x)=x+5`

(a) We have to write the expression for given composition

`g(f(4))`

Now first we find f(4)

So f(4) =
`4^2=16`

So
`g(f(4))=g(16)=16+5=21`

(b)
`f(g(4))`

Now first we find g(4)

So g(4) =
`4+5=9`

So
`f(g(4))=f(9)=9^2=81`

`(fog)x=(x+5)^2=x^2+10x+25`