Answer
(a) $22$
(b) $f(-x)=x^2-5x-2$
(c) $-f(x)=-x^2-5x+2$
(d) $f(3x)=(3x)^2+5(3x)-2=9x^2+15x-2$
(e) $\frac{f(x+h)-f(x)}{h}=2x+h+5$
Work Step by Step
(a) Given $f(x)=x^2+5x-2$, we have $f(3)=(3)^2+5(3)-2=22$
(b) We have $f(-x)=x^2-5x-2$
(c) We have $-f(x)=-x^2-5x+2$
(d) We have $f(3x)=(3x)^2+5(3x)-2=9x^2+15x-2$
(e) We have $f(x+h)=(x+h)^2+5(x+h)-2=x^2+2xh+h^2+5x+5h-2$ and $\frac{f(x+h)-f(x)}{h}=\frac{2xh+h^2+5h}{h}=2x+h+5$
