Let f and g be two invertible functions. Prove that a.) (fog) is an invertible function. b.) (fog) ^{-1}(x) = (g^{-1} o f^{-1})(x). Explain how you can determine if two n x n matrices, A and B, are inverses. Gi
To find the inverse of a trigonometric function, it pays to know about all the trig functions and their inverses. For example, if you want to find the inverse of y = sin(x), you need to know that the inverse of the sine function is the arcsine function; no simple al...
There will be times when they give you functions that don't have inverses, and, from the graph of the given function, it's easy to see that this function can't possibly have an inverse, since it violates the Horizontal Line Test: It is usually considered acceptable to draw the above ...
These two functions are inverses of each other: Properties of the Natural Exponential Function ex has some handy properties that make it very easy to manipulate algebraically. Because of the laws of exponents, we know that: Why Use Natural Exponential Functions? We don’t just use the natural ...
How to understand multiplicative inverses? Find the convolution f(t)*g(t) given f(t)=1, g(t)=cos 2t. Why is the integral a linear operator? If f ( x ) and g ( x ) are inverse functions of each other, which of these equations does not always hold? a. g ( f ( x ) ) =...
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It seems like a silly question to ask, but we're still not entirely sure whata black hole's compositionis or what its main functions are. Some theorize our universe may even be inside a black hole. Right now, the most accepted theory is that they're a clump of matter so dense that...
(partition functions) associated to thermal quantities. Brute force approaches to compute these integrals require a prohibitive effort (see Sect.3) and the founding fathers of computational physics proposed an alternative approach: (i) one introduces a model of the real system, a computational system...
A separate analysis (available upon request) is conducted on a sample of salespeople who go on to become sales managers, where sales jobs—whether sales manager or salesperson—are treated as one occupation. The analysis yields results consistent with the main findings of the paper. We thank an...
How to find the inverse of tan(x) What is the inverse of a cubed number? Are the following functions inverses of each other? f(x) = 10x-20 and g(x) = 1x+2 How do you figure out inverse matrices? Use f(x) = 3x^2+ 2x- 4 and g(x) =x- 2 t...