Question

Given that f(x) = x2 + 4x and g(x) == x + 6, calculate(a) (fog)(x)=(b) (go f)(x)=(c) (fof)(x)=(d) (gog)(x)=

Answer 1

To calculate the given function:

`\begin{gathered} f(x)=x^2+4x \\ g(x)=x+6 \end{gathered}`

(a) (fog)(x) = f(g(x))=

`\begin{gathered} f(x+6)=(x+6)^2+4(x+6) \\ =x^2+12x+36+4x+24 \\ =x^2+16x+60 \end{gathered}`

(b) (gof)(x) = g(f(x))=

`g(x^2+4x)=x^2+4x^{}+6`

(c) (fof)(x) = f(f(x))=

`\begin{gathered} f(x^2+4x)=(x^2+4x^{})^2+4(x^2+4x) \\ =(x^2+4x)(x^2+4x)+4x^2+16x \\ =x^4+8x^3+16x^2+4x^2+16x \\ =x^4+8x^2+20x^2+16x \end{gathered}`

(d) (gog)(x) = g(g(x)=

`\begin{gathered} g(x+6)=(x+6)+6 \\ =x+12 \end{gathered}`