SOLUTION: Hi, Can you help me with this math problem? If f is one-to-one find and equation for its universe. f(x)=x^3-5

Question 134223: Hi, Can you help me with this math problem?
If f is one-to-one find and equation for its universe.
f(x)=x^3-5
Answer by nycsharkman(136) (Show Source): You can put this solution on YOUR website!
If f is one-to-one find an equation for its inverse.
f(x)= x^3 - 5.
Why did you call this a rational function? Where is the fraction?
You can only call a function rational if there is a fraction.
We need to find the inverse of the given function.
f(x) = x^3 - 5
First, replace f(x) with y because y is the same as f(x). In other words, they are interchangeable math symbols.
y = x^3 - 5
Secondly, switch the x and y letters places.
x = y^3 - 5
Add 5 to x.
x + 5 = y^3
Take the CUBE ROOT of both sides.
CUBEROOT{x + 5} = CUBEROOT{y^3}
CUBEROOT{x + 5} = y
Replace y with the inverse notation (the symbol), which is f^-1(x).
f^-1(x) = CUBEROOT{x + 5}

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