Question 903481
When you have {{{f^-1}}} it means that the question is asking you to find the {{{inverse}}}. This means that the original function {{{f(x)=2x^3-7}}} is reflected along the line {{{y=x }}}.
 
so, what you do is change all the {{{x}}} values to {{{y}}} values and all the {{{y}}} values to {{{x}}} values({{{f(x)}}} is also known as {{{y}}})
 
if {{{y=2x^3-7}}} then {{{f(x)^-1}}} is:
 
 {{{x=2y^3-7}}}

 solve for {{{y }}}

 {{{x+7=2y^3}}}

{{{(x+7)/2=y^3}}}

{{{ root(3,(x+7)/2) =y}}}


 so {{{f(x)^(-1) = root(3,(x+7)/2) }}} or {{{f(x)^(-1) = root(3,(x+7))/root(3,2))}}}