to solve for the inverse
1. replace f(x) with y
2. switch x and y
3. solve for y
4. replace y with f⁻¹(x)
so
[tex]f(x)=\frac{2x-3}{5}[/tex]
replace f(x) with y
[tex]y=\frac{2x-3}{5}[/tex]
switch x and y
[tex]x=\frac{2y-3}{5}[/tex]
times both sides by 5
[tex]5x=2y-3[/tex]
add 3 to both sides
[tex]5x+3=2y[/tex]
divide by 2
[tex]\frac{5x+3}{2}=y[/tex]
[tex]y=\frac{5x+3}{2}[/tex]
repace y with f⁻¹(x)
[tex]f^{-1}(x)=\frac{5x+3}{2}[/tex]
D is the answer
