Hello,
[tex] 1)\\
f(x)=x-5\\
g(x)=x^2+1\\
(fog)(x)=f(g(x))=f(x^2+1)=5-(x^2+1)=5-x^2-1=4-x^2\\
Answer\ A\\\\
2)\\
f(x)=5x\\
g(x)=2x+1\\
(gof)(-1)=g(f(-1))=g(-5)=-10+1=-6\\
Answer\ B\\\\
3)\\
f(x)=2x^2-3x\\
\dfrac{f(x+h)-f(x)}{h}\\
=\dfrac{2(x+h)^2-3(x+h)-(2x^2-3x) }{h}\\
=\dfrac{2(x^2+2xh+h^2)-3x-3h-2x^2+3x }{h}\\
=\dfrac{4xh+2h^2-3h}{h}\\
=4x+2h-3\\
Answer\ A\\\\
4)\\
f(x)=\sqrt{x-3}\\
g(x)=\sqrt{2x}\\
(f+g)(x)=\sqrt{x-3}+\sqrt{2x}\\
Answer\ A\\\\
5)\\
f(x)=x-5\\
g(x)=x^2+1\\
[/tex]
[tex] (gof)(x)=g(f(x))=g(x-5)=(x-5)^2+1=x^2-10x+26\\
Answer\ D\\
[/tex]
