SOLUTION: Given f(x)=-sqrt(1-x), determine f^-1(x)

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Question 164428: Given f(x)=-sqrt(1-x), determine f^-1(x)
Found 2 solutions by jim_thompson5910, padmameesala:
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
f%28x%29=-sqrt%281-x%29 Start with the given function


y=-sqrt%281-x%29 Replace f(x) with y


x=-sqrt%281-y%29 Switch x and y


-x=sqrt%281-y%29 Multiply both sides by -1


x%5E2=1-y Square both sides.


x%5E2%2By=1 Add y to both sides


y=1-x%5E2 Subtract x%5E2 from both sides


y=-x%5E2%2B1 Rearrange the terms.


So the inverse function is f%5E-1%28x%29=-x%5E2%2B1

Note: the domain and range of f%28x%29=-sqrt%281-x%29 is x%3C=1 and y%3C=0

So this means that the domain and range of f%5E-1%28x%29=-x%5E2%2B1 is x%3C=0 and y%3C=1

Answer by padmameesala(42) About Me  (Show Source):
You can put this solution on YOUR website!
let f(x)=y then x=f^-1(y)
given f(x)= -sqrt(1-x)
that is y = -sqrt(1-x)
squaring on both sides we get, y^2 = 1-x
x = 1-y^2 and x = f^-1(y)
so f^-1(y) = 1-y^2
hence f^-1(x) = 1-x^2