# SOLUTION: For the function defined by f(x)=2-x^2, 0 is < and = to x, I need to find a formula for f^-1(x). This is real frustrating...

Algebra ->  Algebra  -> Logarithm Solvers, Trainers and Word Problems -> SOLUTION: For the function defined by f(x)=2-x^2, 0 is < and = to x, I need to find a formula for f^-1(x). This is real frustrating...      Log On

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 Click here to see ALL problems on logarithm Question 65650: For the function defined by f(x)=2-x^2, 0 is < and = to x, I need to find a formula for f^-1(x). This is real frustrating...Answer by praseenakos@yahoo.com(507)   (Show Source): You can put this solution on YOUR website!QUESTION: f(x)=2-x^2, 0 is < and = to x, I need to find a formula for f^-1(x). ANSWER: f(x)=2-x^2 For our convenience, lets take, y = 2-x^2 Rewrite the given equation as follows. Add x^2 to both sides of the equation, ==> y + x^2 = 2-x^2 + x^2 ==> x^2 + y = 2 Subtract y from both sides of the equation, ==> x^2 + y - y = 2 - y ==> x^2 = 2 - y Take square root on both sides of the expression, ==> x = square root of ( 2 - y) We can write this expressions(after replacing y by x ) as, f-1(x) = sqrt (2-x) Which is the required inverse function. Here we can see that this inverse function is not defined when the value of x is greater than 2 because then 2-x becomes a negative number and sqrt of a negative number cannot be determined. So we can write, inverse of the given function is sqrt of (2-x) and x is less than or equal to 2. Hope you Understood. Regards. praseenakos@yahoo.co.in