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
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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) (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).
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