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) About Me  (Show Source):
You can put this solution on YOUR website!
f%28x%29=-3%2Bsqrt%28-9%29%2B6x
f%5E-1%28x%29=?
y=-3%2Bsqrt%28-9%29%2B6x
Invert
x=-3%2Bsqrt%28-9%29%2B6y
Solve for y
6y=3-sqrt%28-9%29-x
y=%283-sqrt%28-9%29-x%29%2F6
So
If f%28x%29=-3%2Bsqrt%28-9%29%2B6x
Then f%5E-1%28x%29=%283-sqrt%28-9%29-x%29%2F6

Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
I'm assuming that the function is f%28x%29=-3%2Bsqrt%28-9%2B6x%29


f%28x%29=-3%2Bsqrt%28-9%2B6x%29 Start with the given function.


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


y=-3%2Bsqrt%28-9%2B6x%29 Replace f(x) with y


x=-3%2Bsqrt%28-9%2B6y%29 Swap each x and y. The goal now is to solve for y to find the inverse.


x%2B3=sqrt%28-9%2B6y%29 Add 3 to both sides.


%28x%2B3%29%5E2=%28sqrt%28-9%2B6y%29%29%5E2 Square both sides (to undo the square root)


%28x%2B3%29%5E2=-9%2B6y Square the square root to eliminate it.


x%5E2%2B6x%2B9=-9%2B6y FOIL


x%5E2%2B6x%2B9%2B9=6y Add 9 to both sides.


x%5E2%2B6x%2B18=6y Combine like terms.


%28x%5E2%2B6x%2B18%29%2F6=y Divide both sides by 6.


y=%28x%5E2%2B6x%2B18%29%2F6 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: [)