SOLUTION: What is the inverse of this function ? f(x)= -√(x+5)+3 Thanks for any help.

Algebra ->  Square-cubic-other-roots -> SOLUTION: What is the inverse of this function ? f(x)= -√(x+5)+3 Thanks for any help.       Log On


   

Question 850038: What is the inverse of this function ?
f(x)= -√(x+5)+3
Thanks for any help.

Found 2 solutions by jim_thompson5910, josgarithmetic:
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
Replace f(x) with y. Then swap x and y. Afterwards, solve for y to find f%5E%28-1%29%28x%29


f%28x%29+=+-sqrt%28x%2B5%29%2B3


y+=+-sqrt%28x%2B5%29%2B3


x+=+-sqrt%28y%2B5%29%2B3


x-3+=+-sqrt%28y%2B5%29


-1%2A%28x-3%29+=+-1%2A%28-sqrt%28y%2B5%29%29


-x%2B3+=+sqrt%28y%2B5%29


3-x+=+sqrt%28y%2B5%29


%283-x%29%5E2+=+y%2B5


%283-x%29%5E2-5+=+y


y+=+%283-x%29%5E2-5


f%5E%28-1%29%28x%29+=+%283-x%29%5E2-5

Answer by josgarithmetic(39623) About Me  (Show Source):
You can put this solution on YOUR website!
Quick way,
x=-sqrt%28y%2B5%29%2B3, roles of x and y were switched. y represents the original f(x), a representation only.
x-3=-sqrt%28y%2B5%29
x%5E2-6x%2B9=y%2B5
y=x%5E2-6x%2B9-5
highlight_green%28y=x%5E2-6x%2B4%29

That is not yet finished. You need to know the vertex, because f(x) was the lower half of a parabola, so the inverse must correspond to that lower half.

Put into standard form.
y=x%5E2-6x+%2B%286%2F2%29%5E2-%286%2F2%29%5E2%2B4-----Completing the Square
y=%28x-3%29%5E2%2B4-9
highlight%28y=%28x-3%29%5E2-5%29-------vertex is (3,-5)
We must include the restriction, highlight%28x%3C=3%29.