Question

Let f(x)=-x-1 and g(x)=x^2-5 Find (f o g)(-2).

Answer 1

A composite function (f o g) (x) is the f[g(x)]

To find (f o g)(-2)

1) Let's find (f o g) (x) by substituing x by x² - 5 in f(x):

`\begin{gathered} f(x)=x-1 \\ (f\circ g)(x)=(x^2-5)-1 \\ (f\circ g)(x)=x^2-5-1 \\ (f\circ g)(x)=x^2-6 \end{gathered}`

2) To find (f o g) (-2), let's substitute x by 2 and solve the equation.

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

Answer: -2.