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

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

Replace f(x) with y

Switch x and y

Multiply both sides by -1

Square both sides.

Add y to both sides

Subtract from both sides

Rearrange the terms.

So the inverse function is

Note: the domain and range of is and

So this means that the domain and range of is and
Answer by padmameesala(42) (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
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