ok so basically for inverse, the input becomes output, output becomes input
f(x)=y
in inverse
f(y)=x
so
f(x)=3x-1/2
y=3x-1/2
f⁻¹(3)=y
f(y)=3
basically, replace f(x) with 3 and solve for x
3=3x-1/2
add 1/2
3.5=3x
divide by 3
1.16666666=x
or
1 and 1/6=x
this might seem like voodo so I will do the normal way
1. replace f(x) with y
2. switch x and y
3. solve for y
4. replace y with f⁻¹(x)
replace
y=3x-1/2
switch
x=3y-1/2
solve
x+1/2=3y
(x+1/2)/3=y
replace
f⁻¹(x)=(x+1/2)/3
f⁻¹(3)=(3+1/2)/3
f⁻¹(3)=(3.5)/3
f⁻¹(3)=1 and 1/6 or 1.1666666
