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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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Calculus 1 / AB

Chapter 2

Limits and Derivatives

Section 5

Continuity

Limits

Derivatives

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04:40

In mathematics, the limit of a function is the value that the function gets very close to as the input approaches some value. Thus, it is referred to as the function value or output value.

In mathematics, a derivative is a measure of how a function changes as its input changes. Loosely speaking, a derivative can be thought of as how much one quantity is changing in response to changes in some other quantity; for example, the derivative of the position of a moving object with respect to time is the object's velocity. The concept of a derivative developed as a way to measure the steepness of a curve; the concept was ultimately generalized and now "derivative" is often used to refer to the relationship between two variables, independent and dependent, and to various related notions, such as the differential.

01:55

Let $f(x)=\left(\frac{1}{x…

01:10

Show $f(x)=x$ is continuou…

01:03

Let $$g(x)=\left\{\begin{a…

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.

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