Answer:
[tex]\implies y =\dfrac{(x-3)^3+3}{5}[/tex]
Step-by-step explanation:
Given :-
- [tex]\sqrt[3]{5x-3}+2[/tex]
And we need to find out the inverse of the function. So for that replace x and y. We have ,
[tex]\implies \sqrt[3]{5x-3}+2[/tex]
On interchanging x and y :-
[tex]\\\\\implies x = \sqrt[3]{5y-3}+2[/tex]
Solve out for y :-
[tex]\implies x -2 =\sqrt[3]{5y-3}\\\\\implies (x-3)^3=5y-3 \\\\\implies 5y = (x-3)^3+3\\\\\implies y =\dfrac{(x-3)^3+3}{5}[/tex]
Hence the inverse of the function is (x-3)³+3/5.
