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Problem 76 Hard Difficulty

(a) Graph the function $ f(x) = \sin (\sin^{-1} x) $ and explain the appearance of the graph.
(b) Graph the function $ g(x) = \sin^{-1} (\sin x) $. How do you explain the appearance of this graph?

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Video Transcript

graphed the function f of X equals sign of arc sine of X and explain the appearance of the graph. So for this question here, notice that this function f simplifies the X, and we all know what you know. X looks like it's, you know, it's a line through the origin with slope one. Okay, but notice that there is going to be a restriction in the domain of ass. Okay, so I suppose I noticed that the domain of the outside function sign for ex belongs to the real numbers. But the inside function, the arc sine of acts there is a restriction in the domain in X belongs from You could have wonder one. I do have this function graft here. Okay? And it's going to take a look at it. And when you have the function, why equals the art? The sign of the arc sine of X, and that does reduce down to X with domain. Ah, in which explosions from negative or from positive one. Ah, negative one. Okay, so we have the same function. Why equals X with the restriction in the domain? Okay, stick a look. A ah, the other one g equals the arc sine the sign of ax. Okay, so and notice we do have, uh, these characters six year in in their respective domains. Okay, let's go in and take a look at this graph here. So we have the ark sign. Signed X. Okay, so we look. Looks like we have these concentric, uh, you know, X negative axe. I'm going to guess this is negative X here. Okay, X in a rex. Thanks for watching.