Question

Could u please help me with 15, 16 and 17?? thank you:)

Answer 1

Given:

15)

`\begin{gathered} f(x)=x^3+4 \\ g(x)=3x^2+7 \\ g(f(x))=g(x^3+4) \\ g(f(x))=3(x^3+4)^2+7 \\ g(f(-1))=3((-1)^3+4)^2+7 \\ g(f(-1))=3(-1+4)^2+7 \\ g(f(-1))=3(3)^2+7 \\ g(f(-1))=34 \end{gathered}`

Answer: option b) 34

16)

`\begin{gathered} f(x)=x^2+3x+2 \\ g(x)=2x^3+1 \\ (f\circ g)(x)=f(g(x)) \\ (f\circ g)(x)=f(2x^3+1) \\ (f\circ g)(x)=(2x^3+1)^2+3(2x^3+1)+2 \\ (f\circ g)(-1)=(2(-1)^3+1)^2+3(2(-1)^3+1)+2 \\ (f\circ g)(-1)=(-2+1)^2+3(-2+1)+2 \\ (f\circ g)(-1)=1-3+2 \\ (f\circ g)(-1)=0 \end{gathered}`

Answer: option c) 0

17)

`\begin{gathered} f(x)=x^2+x+1 \\ g(x)=x+3 \\ f(g(x))=f(x+3) \\ f(g(x))=(x+3)^2+(x+3)+1 \\ f(g(x))=x^2+6x+9+x+4 \\ f(g(x))=x^2+7x+13 \end{gathered}`

Answer: option d)