Question 1179074
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I suspect the given function is supposed to be {{{(x-5)^3}}} ("(x-5)^3") instead of {{{(x-5)3}}} ("(x-5)3")...<br>
In typed text, it is standard to use "^" to denote exponentiation.<br>
The standard method for finding the inverse of a function is to switch the x and y and solve for the new y:<br>
{{{y = (x-5)^3}}} --> {{{x = (y-5)^3}}}<br>
Solve for y....<br>
{{{x = (y-5)^3}}}
{{{x^(1/3) = y-5}}}
{{{y = x^(1/3)+5}}}<br>
ANSWER: the inverse function is {{{f^(-1)(x) = x^(1/3)+5}}}<br>
For a relatively simple function like this, the inverse function can be found much faster using the idea that the inverse function "gets you back where you started" by performing the inverse operations in the opposite order.  For this example, we have....<br>
The given function (a) subtracts 5 and (b) cubes the result<br>
The inverse function must (a) take the cube root and (b) add 5<br>
ANSWER: The inverse function is {{{x^(1/3)+5}}}<br>