In Exercises 101–102, find an equation for f^(-1)(x). Then graph ...

Question

In Exercises 101–102, find an equation for f^(-1)(x). Then graph f and f^(-1) in the same rectangular coordinate system. f(x) = 1 - x^2, x ≥ 0.

Accepted Answer

find the inverse of the given function and the graph, both the function and its inverse in the same coordinate system where f of X equals X. The third not to find the inverse. I'm first going to set us F X equal to y. Other words Y equals X to the third. Now we want to solve in terms of X. So we have extra third and right side on the left side. Let's raise the right side to the power of 1/3 and the left side to the power of 1/3. I will then get why it's the one third equals X. Because three and one third will cancel each other out. Now that we're here, I'm gonna switch my variables back. Other words, I'll say X to the 1/3 equals what. And finally, next 1 3rd it's equal to f inverse of X. So FN vs X. The 1/3. Now, if we were to graph this in the graphing calculator, we'd see the X. The third. It's gonna look like this. X. to the 1/3. It's going to look like this. So you want a graph that has both of these lines on it. If you look here, that's a good answer. A answer. A actually looks like it has both lines that we drew. Let's check B, C and D. Just to be safe. I feel like it be we notice it does not have one of the lines, it doesn't have our ex the one third graph it has a different graph. Look at. See it has an extra one photograph but it's actually flipped the wrong direction. I feel like A. D. The extra one third graf has slipped in the direction and the extra third graf has slipped in the direction. That means the answer to our problem turns out to be answer A Okay. I hope to help you solve this problem. Thank you for watching. Goodbye.

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In Exercises 101–102, find an equation for f^(-1)(x). Then graph f and f^(-1) in the same rectangular coordinate system. f(x) = 1 - x^2, x ≥ 0.