SOLUTION: Hi could you help me with this? Find the inverse of y=sqrtx+9. Is the inverse a function? Thank you

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Question 126726: Hi
could you help me with this?
Find the inverse of y=sqrtx+9. Is the inverse a function?
Thank you
Answer by Earlsdon(6294) About Me  (Show Source):
You can put this solution on YOUR website!
Find the inverse of:
y+=+sqrt%28x%29%2B9 This could be written as:f%28x%29+=+sqrt%28x%29%2B9
To find the inverse of a function, interchange the x and y and solve for y.
x+=+sqrt%28y%29%2B9 Now solve for y by subtracting 9 from both sides.
x-9+=+sqrt%28y%29 Square both sides.
%28x-9%29%5E2+=+y Simplify.
y+=+x%5E2-18x%2B81 Now replace the y with f%5E%28-1%29%28x%29:
f%5E%28-1%29%28x%29+=+x%5E2-18x%2B81 This is the inverse function of f%28x%29+=+sqrt%28x%29%2B9. And...yes, the inverse is a function!
To verify this, use the following rule: f%28f%5E%28-1%29%28x%29%29+=+x
In this case:
f%28f%5E%28-1%29%28x%29%29+=+f%28x%5E2-18x%2B81%29 Replace every x withsqrt%28x%29%2B9 and simplify:
highlight%28%28sqrt%28x%29%2B9%29%5E2%29-highlight%2818%28sqrt%28x%29%2B9%29%29%2B81 Simplify.
highlight%28x%2B18sqrt%28x%29%2B81%29-highlight%2818sqrt%28x%29-162%29%2B81 Combine like-terms.
x%2Bhighlight%2818sqrt%28x%29-18sqrt%28x%29%29%2Bhighlight%2881-162%2B81%29=x