Question 111761
{{{y=(x+2)^3}}} Start with the given equation



{{{x=(y+2)^3}}} Switch x and y


Now let's solve for y



{{{root(3,x)=y+2}}} Take the cube root of both sides



{{{root(3,x)-2=y}}} Subtract 2 from both sides



So our inverse function is {{{g(x)=root(3,x)-2}}}



Now if we graph, we get


{{{ graph( 500, 500, -10, 10, -10, 10, x^(1/3)-2,-(-x)^(1/3)-2) }}} 


So we can see that the domain and range of g is all real numbers (for both of them)