Question

Let f(x) = x^2 and g(x) = 2x + 3. Write an expression that represents each composition:

a. (g ∘ f)(x)
b. f(f(−2))
c. (f ∘ g) (1 / x)

Answer 1

Remember, if f and g are functions then
`(f\circ g)(x)=f(g(x))`, then:

a)
`(g\circ f)(x)=g(f(x)))=g(x^2)=2(x^2)+3=2x^2+3`

b)
`f(f(-2))=f((-2)^2)=f(4)=4^2=16`

c)

`(f \circ g)((1)/(x))=f(g((1)/(x)))\\=f(2((1)/(x))+3)\\=f((2)/(x)+3)\\=((2)/(x)+3)^2\\ =((2)/(x))^2+2*(2)/(x)*3+3^2 \\ =(4)/(x^2)+(12)/(x)+9`

then,
`(f\circ g)=(4)/(x^2)+(12)/(x)+9`