Let p(x) = 2x^3 - 113 and let q be the inverse of p. Find q(137).
Thanks for whoever is going to answer this!!!
Let p(x) = 2x^3 - 113 and let q be the inverse of p. Find q(137)
Note that the inverse just reverses the original coordinates
So the coordinates of the inverse are ( 137, x)
So....putting 137 into the inverse sends us back to the otiginal "x"
So....the original coordinates were ( x, 137 )
And x will equal q (137)
So...all we need to do is to set p = 137 and solve to find this otiginal x
2x^3 - 113 = 137 add 113 to both sides
2x^3 = 250 divide both sides by 2
x^3 = 125 take the cube root of both sides
x = 5 and this is q(137)
Proof...I won't derive it but the inverse q is ∛ [ ( x + 113) / 2 ]
And q (137) = 5