What is the inverse function of x^3 + 1 and how do you find its value at x = 4?

[UrbanXrisis]

I was just doing a problem in a review book and my answer doesn't match with what the books says.

It f(x)=x^3+1 and if f^-1 is the inverse function of f, what is f^-1(4)?

I got an answer of 0.02 but the book says it is 1.44.

All I did was sub in 4 into the equation, which I get 64, then set that under one...1/64 and get 0.02 as the inverse. How did the book get 1.44?

 

[cookiemonster]

You're mistaking the inverse with the reciprocal.

The problem is asking for what value of x will satisfy f(x) = 4.

Clearly f(.002) does not equal 4, but 4(1.44) = 1.44^3 + 1 = 3.985984 ~ 4

cookiemonster

 

[Parth Dave]

The notation is what really confuses people most of the time. The inverse of a function basically switches the x and y values. If you want to find the inverse for a function than all you would have to do is switch the values. In other words, replace all the x's with y's and vice versa. Than solve for y (assuming you originally had a y= equation) and you will have your inverse function. Than you can just plug your value in. In this case it would be:
y = x^3 + 1
For the inverse:
x = y^3 + 1
y = (x - 1) ^ (1/3)
so f^-1(4) = (4 - 1) ^ (1/3) = 3 ^ (1/3) ~ 1.44