Question

Let f(x) = 2x - 1 and g(x) = x² + 1. Find and simplify: (g ° ƒ) (1/2)

Answer 1

To find the composition we need, let's first find the general expression:

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

Hence:

`(g\circ f)(x)=4x^2-4x+2`

Now we can evaluate when x=1/2:

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

Therefore:

`(g\circ f)((1)/(2))=1`