Answer
(a) $f(3)=22$
(b) $f(-x)=x^2-5x-2$
(c) $-f(x)=-x^2-5x+2$
(d) $f(3x)=9x^2+15x-2$
(e) $\dfrac{f(x+h)-f(x)}{h}=h+2x+5$
Work Step by Step
(a) $f(3)=3^2+5(3)-2=9+15-2=22$
(b) $f(-x)=(-x)^2+5(-x)-2=x^2-5x-2$
(c) $-f(x)=-(x^2+5x-2)=-x^2-5x+2$
(d) $f(3x)=(3x)^2+5(3x)-2=9x^2+15x-2$
(e) $\dfrac{f(x+h)-f(x)}{h}=$
$\dfrac{(x+h)^2+5(x+h)-2-(x^2+5x-2)}{h}=$
$\dfrac{x^2+2xh+h^2+5x+5h-2-x^2-5x+2}{h}=$
$\dfrac{h^2+2xh+5h}{h}=$
$\dfrac{h(h+2x+5)}{h}=$
$h+2x+5$
