Answer
a) $-3$; b) $x^2-4x-2$; c) $x^2+4x+1$; d) $-x^2+4x-1$; e) $x^2-3$; f) $2x+h-4$
Work Step by Step
We are given the function:
$f(x)=x^2-4x+1$
a) Compute $f(2)$:
$f(2)=2^2-4(2)+1=-3$
b) Compute $f(x)+f(2)$:
$f(x)+f(2)=x^2-4x+1-3=x^2-4x-2$
c) Compute $f(-x)$:
$f(-x)=(-x)^2-4(-x)+1=x^2+4x+1$
d) Compute $-f(x)$:
$-f(x)=-(x^2-4x+1)=-x^2+4x-1$
e) Compute $f(x+2)$:
$f(x+2)=(x+2)^2-4(x+2)+1$
$=x^2+4x+4-4x-8+1$
$=x^2-3$
f) Compute for $h\not=0$:
$\dfrac{f(x+h)-f(x)}{h}=\dfrac{(x+h)^2-4(x+h)+1-(x^2-4x+1)}{h}$
$=\dfrac{x^2+2hx+h^2-4x-4h+1-x^2+4x-1}{h}$
$=\dfrac{2hx+h^2-4h}{h}$
$=\dfrac{h(2x+h-4)}{h}$
$=2x+h-4$
