Question

Consider these functions:/(=) =-{=2 + 51g(I) = =2 + 2What is the value of fg(-2))?

Answer 1

Answer: Provided the two functions, f(x) and g(x), we have to find the composite of these two functions at x = - 2:

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

The composite function is as follows:

`\begin{gathered} f(g(x))=-(1)/(2)(x^2+2)^2+5(x^2+2) \\ \\ \\ f(g(x))=-(1)/(2)[x^4+4x^2+4]+5x^2+10 \\ \\ \\ f(g(x))=-(x^4)/(2)-2x^2-2+5x^2+10 \\ \\ f(g(x))=-(x^4)/(2)-2x^2-2+5x^2+10 \\ \\ \\ f(g(x))=-(x^4)/(2)+3x^2+8 \\ \\ \\ f(g(-2))=-((-2)^4)/(2)+3(-2)^2+8 \\ \\ \\ f(g(-2))=-((-2)^4)/(2)+3(-2)^2+8=-8+12+8=12 \\ \\ \\ f(g(-2))=12 \end{gathered}`

The answer is 12.