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...

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

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