Answer:
[tex](h-f)(x) = x^2-x+2\\[/tex]
[tex](f+h)(x) = x^2+x-2[/tex]
[tex](g-f)(x) = x+5[/tex]
[tex](g+h)(x) =x^2+2x+3[/tex]
Step-by-step explanation:
Function composition is an operation that takes two functions and produces a third function.
The composite function (f + g)(x) means to add function f(x) and function g(x).
The composite function (f - g)(x) means to subtract function g(x) from function f(x).
Given functions:
[tex]\begin{cases}f(x)=x-2\\g(x)=2x+3\\h(x)=x^2\end{cases}[/tex]
Therefore:
[tex]\begin{aligned}(h-f)(x) & = h(x) - f(x)\\& = x^2-(x-2)\\& = x^2-x+2\end{aligned}[/tex]
[tex]\begin{aligned}(f+h)(x) & = f(x)+h(x)\\& = x-2+x^2\\& = x^2+x-2\end{aligned}[/tex]
[tex]\begin{aligned}(g-f)(x) & = g(x)-f(x)\\& = 2x+3-(x-2)\\& = 2x+3-x+2\\& = 2x-x+3+2\\& = x+5\end{aligned}[/tex]
[tex]\begin{aligned}(g+h)(x) & = g(x)+h(x)\\& = 2x+3+x^2\\& = x^2+2x+3\end{aligned}[/tex]
Learn more about composite functions here:
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