Question

Find (f o g) (x) if g(x) = x + 1 and f(x) = 2x^2 - 5x + 8

Answer 1

Given:

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

The composition of the given two function is,

$\begin{gathered} (f\circ g)(x)=f(g(x)) \\ =f(x+1) \\ =2(x+1)^2-5(x+1)+8\ldots\ldots\ldots.(\text{ apply the definition f(}x)) \\ =2x^2+4x+2-5x-5+8 \\ =2x^2-x+5 \end{gathered}$

Answer:

$(f\circ g)(x)=2x^2-x+5$