Answer
a) $\dfrac{1}{4}$; b) $\left(\dfrac{1}{4},\infty\right)$; c) $1$; d) $(-\infty,1]$; e) see graph
Work Step by Step
We are given the functions:
$f(x)=4x-1$
$g(x)=-2x+5$
a) Solve $f(x)=0$
$4x-1=0$
$4x=1$
$x=\dfrac{1}{4}$
b) Solve $f(x)>0$
$4x-1>0$
$4x>1$
$x>\dfrac{1}{4}$
$\left(\dfrac{1}{4},\infty\right)$
c) Solve $f(x)=g(x)$
$4x-1=-2x+5$
$6x=6$
$x=1$
d) $f(x)\leq g(x)$
$4x-1\leq -2x+5$
$4x-1+2x\leq -2x+5+2x$
$6x-1\leq 5$
$6x-1+1\leq 5+1$
$6x\leq 6$
$x\leq 1$
$(-\infty,1]$
e) Graph $f(x)$ and $g(x)$ and find the intersection, which is the solution of the equation $f(x)=g(x)$:
$x=1$
