Question

Given that F(x)=6x+4 and g(x)=4-x^2, calculate (a) F(g(0))=(b) g(F(0))=

Answer 1

Given the functions below

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

a) For F(g(0))

Firstly, F(g(x) will give

`\begin{gathered} \left(F∘g\right)\left(x\right)=F\mleft(g\mleft(x\mright)\mright)=6(4-x^2)+4=24-6x^2+4=28-6x^2 \\ F(g(x))=28-6x^2 \\ F(g(0))=28-6(0)^2=28-0=28 \\ F(g(x))=28 \end{gathered}`

Hence, F(g(0)) is 28

b) For g(F(0))

Firstly, g(F(x) will give

`\begin{gathered} g\mleft(F(x)\mright)=4-(6x+4)^2=4-36x^2-48x-16=-36x^2-48x-12 \\ g(F(0))=-36(0)^2-48(0)-12=0-0-12=-12 \\ g(F(x))=-12 \end{gathered}`

Hence, g(F(0)) is -12