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Numerade Educator

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Problem 48 Easy Difficulty

Let $ f(x) = 1/x $ and $ g(x) = 1/x^2 $.

(a) Find $ (f \circ g)(x) $.
(b) Is $ f \circ g $ continuous everywhere? Explain.

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Video Transcript

This is problem number 48 of the Stuart Calculus eighth edition section 2.5 mhm that have of X equal one over X and you have X equals one over X word party. Find f of G of X. And if you recall, this is the same as the function G plugged into the function of F. That's what this notation means. So we will do just that for party F of a gene would be one to either by and since, Yeah, function has an X here in denominator. This new function G will go where the X is for the function F, and therefore it would be one over X squared in the denominator. And if we rearrange this one divided by this is the same as one divided by or one multiplied by the reciprocal. In a much simpler sense, the final function is X squared, and that is what this sequence here F G composite function party is. F of Jean continues everywhere explain now, if we take a look at F M G, the function is X squared. It's a polynomial, and we're tempted to say that the functions continuous everywhere for that reason, however, this is a composite function, two different functions, both of which I did not have X in their domain. So because that's how they started out there, there was a discontinuity for each function at X equals zero. Then we say that effigy is also not also has a discontinuity at this continuity and X equals zero, so it is not continuous everywhere.