Question

Given f(x)=-2x^2+4x+6 and g(x)=2x-3. Find f(g(2))

Answer 1

The Composite Function:

Given:

`\begin{gathered} f(x)=-2x^2+4x+6 \\ g(x)=2x-3 \end{gathered}`

It's required to find f(g(2)).

The composite function uses one of the functions and gets it inside of the second function, that is, f(g(x)) is the function f evaluated in g.

First, compute g(2):

`\begin{gathered} g(2)=2\cdot2-3 \\ g(2)=4-1 \\ g(2)=1 \end{gathered}`

Now we take this value and substitute it in f(x):

`\begin{gathered} f(g(2))=f(1) \\ f(g(2))=-2\cdot1^2+4\cdot1+6 \end{gathered}`

Calculating:

`\begin{gathered} f(g(2))=-2+4+6 \\ f\mleft(g\mleft(2\mright)\mright)=8 \end{gathered}`

Answer: 8