Question

F(x) = x^2 + 5 and g(x) = 6x - 15 find (g•f)(2)

Answer 1

`\begin{gathered} f(x)=x^2+5 \\ g(x)=6x-15 \end{gathered}`

Composition of functions:

`(g\circ f)(x)=g(f(x))`
`(g\circ f)(x)=6(x^2+5)-15`
`\begin{gathered} (g\circ f)(x)=6x^2+30-15 \\ (g\circ f)(x)=6x^2+15 \end{gathered}`

Evaluate to x=2:

`\begin{gathered} (g\circ f)(2)=6(2)^2+15 \\ (g\circ f)(2)=6\cdot4+15 \\ (g\circ f)(2)=24+15 \\ (g\circ f)(2)=39 \end{gathered}`

Then, (g•f)(2) is:

`(g\circ f)(2)=39`