Question

Write the equation of the linear function for which f(0)=3 and f^-1(0)=-2

Answer 1

We know that if f(a)=b then $f^{-1}(b)=a$
and
if $f^{-1}(a)=b$ then f(b)=a
so


since $f^{-1}(0)=-2$ therefor, f(-2)=0

we have 2 points, (-2,0) and (0,3)

we can use slope intercept form
y=mx+b
m=slope
b=y intercept

we have when x=0, y=3, that is the y intercept
y=mx+3

substitute the other point
(-2,0)
x=-2, y=0
0=-2m+3
-3=-2m
divide both sides by -2
$\frac{3}{2}=m$


the equation is
$y=\frac{3}{2}x+3$
or
3x-2y=-6 in standard form
<span />