Question

Evaluate each composition.a) f(x)= 4x+3 and g(x)=x^2Find f(g(1)) and g(f(1))b) f(x)= x–1 and g(x) = x^2+2x–8Find f(g(2)) and g(f(2))

Answer 1

Answer:

a.

`\begin{gathered} f(g(1))=7 \\ g(f(1))=49 \end{gathered}`

b.

`\begin{gathered} f(g(2))=-1 \\ g(f(2))=-5 \end{gathered}`

Step-by-step explanation:

a.

Given that:

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

Then

`\begin{gathered} f(g(x))=4x+3^{}_{} \\ g(f(x))=(4x+3)^2 \\ \end{gathered}`

Using these

`\begin{gathered} f(g(1))=4(1)+3=7 \\ g(f(1))=(4(1)+3)^2=7^2=49 \end{gathered}`

b.

`\begin{gathered} f(x)=x-1 \\ g(x)=x^2+2x-8 \end{gathered}`
`\begin{gathered} f(g(x))=x^2+2x-8-1 \\ =x^2+2x-9 \\ \\ g(f(x))=(x-1)^2+2(x-1)-8 \end{gathered}`

Now

`\begin{gathered} f(g(2))=2^2+2(2)-9 \\ =-1 \\ \\ g(f(2))=(2-1)^2+2(2-1)-8 \\ =1^2+2-8 \\ =-5 \end{gathered}`