SOLUTION: Hello! Find the inverse function of f. f(x) = -3 + √-9+ 6x thanks for your help!

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Question 198357: Hello!
Find the inverse function of f.
f(x) = -3 + √-9+ 6x
thanks for your help!
Found 2 solutions by arallie, jim_thompson5910:
Answer by arallie(162)   (Show Source): You can put this solution on YOUR website!

=?

Invert

Solve for y


So
If
Then
Answer by jim_thompson5910(35256)   (Show Source): You can put this solution on YOUR website!
I'm assuming that the function is


Start with the given function.


Take note that the domain is [) and the range is [) (graph the function if you are not sure)


Replace f(x) with y


Swap each x and y. The goal now is to solve for y to find the inverse.


Add 3 to both sides.


Square both sides (to undo the square root)


Square the square root to eliminate it.


FOIL


Add 9 to both sides.


Combine like terms.


Divide both sides by 6.


Rearrange the equation.


So the inverse function is


Now because the domain and range for f(x) was [) and the range is [), this means that the domain and range for the inverse are:


Domain: [)
Range: [)
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