Question

F(x) = 2x^2 and g(x) = 3x+4 find: (g o f) (5)

Answer 1

Recall the definition of the composition between two functions:

`(g\circ f)(x)=g(f(x))`

Then, to find (g o f) (5), evaluate g at f(5).

`\begin{gathered} f(x)=2x^2 \\ \Rightarrow f(5)=2(5)^2=2\cdot25=50 \end{gathered}`
`\begin{gathered} g(x)=3x+4 \\ \Rightarrow g(50)=3(50)+4=150+4=154 \end{gathered}`

Therefore:

`(g\circ f)(5)=g(f(5))=g(50)=154`

Then, the value of (g o f) evaluated at 5 is 154.