Answer
a. $x=\pm1 $
b. $x=-\frac{1}{4}$
c. $x=0$ or $x=-4$
d. $-1-4$
g. $x=0$
Work Step by Step
$f(x)=-x^2+1,$
$g(x)=4x+1,$
a.$f(x)=-x^2+1=0,$
$-x^2=-1,$
$x^2=1,$
$x=\pm1 $
b.$g(x)=4x+1=0,$
$4x=-1,$
$x=-\frac{1}{4}$
c. $-x^2+1=4x+1,$
$-x^2-4x=0,$
$-x(x+4)=0,$
$x=0$ or $x+4=0, x=-4$
d.$f(x)=-x^2+1>0,$
$-x^2>-1,$
$x^2<1,$
$x<\pm 1$
e. $g(x)\leq 0,$
$4x+1\leq 0,$
$4x\leq -1,$
$x\leq -\frac{1}{4},$
f.$-x^2+1>4x+1,$
$-x^2-4x>0,$
$-x(x-4)>0,$
$x<0$ or $x>-4$
g. $f(x)\geq1,$
$-x^2+1\geq 1,$
$-x^2\geq 0,$
$x=0$
