Question

3. Find the composition (fog)(-2) for the functions f(x) = 2x+1 and g(x)=x²-3

Answer 1

3

Explanation:

Given functions:

`\begin{cases}f(x)=2x+1\\g(x)=x^2-3\end{cases}`

Function composition is an operation that takes two functions and produces a third function.

The given composite function f o g(-2) means to substitute the function g(-2) in place of the x in function f(x):

`\begin{aligned}(f \circ g)(-2)&=f[g(-2)]\\&=2[g(-2)]+1\\&=2(2^2-3)+1\\&=2(4-3)+1\\&=2(1)+1\\&=2+1\\&=3\end{aligned}`