The inverse of this function is f(x) = [tex] \frac{x + 3}{5} [/tex].
You can find the inverse to any function by switching the x and f(x) values. After that, solve for the new f(x) value. The result will be the inverse function. The step-by-step process for this one is done below for you.
f(x) = 5x - 3 ----> Switch the x and f(x) values
x = 5f(x) - 3 ----> Add 3 to both sides
x + 3 = 5f(x) ----> Divide both sides by 5
[tex] \frac{x + 3}{5} [/tex] = f(x) ----> Switch the order for formatting purposes
f(x) = [tex] \frac{x + 3}{5} [/tex]
And that would be your inverse function.
