ANSWER
[tex]\frac{5x - 6}{2}[/tex]
EXPLANATION
The given function is
[tex] \frac{2x + 6}{5} [/tex]
Let
[tex]y = \frac{2x + 6}{5} [/tex]
Interchange x and y.
[tex]x= \frac{2y + 6}{5} [/tex]
Solve for y.
5x=2y+6
5x-6=2y
Divide both sides by 2
[tex] \frac{5x - 6}{2} = y[/tex]
Hence the given function has inverse
[tex]\frac{5x - 6}{2}[/tex]
