Question 1089765
.
<pre>
p(x) = 2x^3 - 113 is shifted x^3.

    Therefore, it is one-to-one function over the entire domain {{{-infinity}}} < x < {{{infinity}}} and maps the real number line by an one-to-one way onto itself.


To find the inverse function, express first x via p:

x = {{{root(3,(p+113)/2)}}}


and then replace x by y and p by x. You will get the expression for the inverse function 

y = {{{root(3,(x+113)/2)}}}.     (1)


To calculate y(137), simply substitute 137 instead of x into the formula (1). You will get

y = {{{root(3,(137+113)/2)}}} = {{{root(3,125)}}} = 5.
</pre>

<U>Answer</U>. &nbsp;The value under the question is &nbsp;5.