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Let f(x) = sqrt(1 - x^2)

0<= x <= 1

(a) Find f^-1. How is it related to f?

(b) identify the graph of F and explain your answer to part (a)

Added Mon, 08 Jun '15

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(a) Find f^-1. How is it related to f?

To find the inverse of F, solve f for x.

first replace f(x) with y for comfort.

y = sqrt(1 - x^2)

>> y^2 = 1 - x^2

>> x^2 = 1 - y^2

>> x = sqrt(1-y^2)

How is it related to f?

The values of the inverse function and the function are the same through the interval.

(b) identify the graph of F and explain your answer to part (a)

On the interval of [0,1] this function forms a quarter circle in the first quadrant.

If you transform the graph by rotating it 90 degreese clockwise and then reflecting it about the x-axis, you find the same graph of F.

Therefore the inverse of F is equal to F

Added Mon, 08 Jun '15

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