Answer:
no
Step-by-step explanation:
The function f(x) does not pass the horizontal line test, so has no inverse, except on a restricted domain. The question does not include any restriction on the domain, so the functions are not inverses of each other.
If we assume your functions are ...
[tex]f(x)=5x^2+3\\\\g(x)=\sqrt{\dfrac{x-3}{5}}[/tex]
Then the value of g(f(x)) is ...
[tex]g(f(x))=\sqrt{\dfrac{(5x^2+3)-3}{5}}=\sqrt{\dfrac{5x^2}{5}}=\sqrt{x^2}[/tex]
This is only equal to x when x ≥ 0. For x < 0, g(f(x)) ≠ x, so the functions are not inverses.
_____
You can see from the graph that the function g(x) is not the reflection of f(x) across the line y=x. If the functions were inverses, each would be a reflection of the other.
