Find the inverse of this function.
y = x^3/4 + x - 1
x = y^3/4 + y - 1
x + 1 = y^3/4 + y
x + 1 = (1/4)y[y^2 + 4]
Where do I go from here?
Multiply both sides by 4 and let . We want to satisfy the following system of equations: and .
Replacing the , and the coefficient for , we have:
That is obviously true. So, let's solve the system of equations:
and . Solving for in the second equation, we can plug it into the first:
Simplifying, we get . We can now solve for by plugging it into the quadratic equation:
Take the cube root of both sides, and you have . Plug that in for , and that gives you . Then, .
(This is the general method for solving a cubic equation).
I thank you for your reply but this question is from a precalculus textbook. The answer cannot be so complicated at this level of learning.
I am to interchange x and y and then isolate y. Finally, I am to replace y with the inverse notation. After all of this, I am to evaluate the inverse by letting x be 1/2.
Here is Wolfram Alpha's answer: here.
It gives the complete answer. I only gave you part of the answer. In general, cubic equations are extremely messy. If that came from a precalc textbook, then my guess is that you should state that the inverse function is too messy to calculate.