SOLUTION: Can you help me with For what domain are f(x) = x^2 and g(x)=√x inverse functions? Make sure you use set builder notation. Explain how you can tell that f(x) = x3 and g(x

Algebra ->  Rational-functions -> SOLUTION: Can you help me with For what domain are f(x) = x^2 and g(x)=√x inverse functions? Make sure you use set builder notation. Explain how you can tell that f(x) = x3 and g(x      Log On


   

Question 1105778: Can you help me with For what domain are f(x) = x^2 and g(x)=√x inverse functions? Make sure you use set builder notation.
Explain how you can tell that f(x) = x3 and g(x)= ∛x are inverse functions. Use complete sentences.
Thank you so much!!!!
Answer by Theo(13342) About Me  (Show Source):
You can put this solution on YOUR website!
set f(x) = y.

your normal function becomes y = x^2.

to derive the inverse function, set x equal to y and y equal to x.

example:

start with f(x) = x^2

let y = f(x).

your normal function becomes y = x^2.

replace y with x and x with y to get x = y^2.

solve for y to get y = plus or minus sqrt(x).

that's your inverse function.

let y = f^-1(x).

your inverse function becomes f^-1(x) = plus or minus sqrt(x).

f(x) = x^2 is your normal function.
f^-1(x) = plus or minus sqrt(x) is your inverse function.

when you graph the function, you set y = f(x).
this allows it to be graphed based on the usual rules of graphing software.

the graph of y = x^2 is shown below:

$$$

the graph of y = plus or minus sqrt(x) is shown below:

$$$

note that the graph of y = plus or minus sqrt(x) is really two equations.

the first equation is y = sqrt(x).
the second equation is y = -sqrt(x).