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 The Inverse of a Function, a selection of answers from the Dr. Math archives. Inverses What is an inverse? Inverse Statements Say there are 3 + 4 times as many girls as boys. Is this the same as saying there are -3 + 1/4 as many boys as girls? Inverting Functions To find the inverse of a function y=f(x), do I interchange the variables x and y, or do I solve for x in terms of y? Inverse Functions in Real Life I would like to know if you have a good example of how inverse functions would be used in real life. Is the Function Invertible? For the following functions f(x) decide if the function is invertible as a function from R to R... Invertible Functions Consider as a function from R -> R (Real) and say whether the function is invertible: h(x) = (sgn x)* sqrt(abs(x)) where sgn is +1 if x is positive, -1 if x is negative, and 0 if x is 0. Finding an Inverse Function What is the inverse function of f(x) = 1 - 2x? What is the general method for finding an inverse function? Is the Inverse a Function? How do I find the inverses and determine whether the inverses are functions? Unraveling an Inverse Function I got this question wrong: y = (-5x - 2) / (-x + 1). Function Its Own Inverse Show that f(x) = X/X-1 is its own inverse. Inverses of Trigonometric Functions How can the functions cosine and sine have inverses of arcsin and arccos respectively? Inverse Functions: Arcsec(x) If y = arcsec(x) then what does x equal? How is this problem related to inverse functions? Inverse of a Function vs. Inverse Proportionality Finding the inverse of a function and graphing yields a graph that has been reflected in the line y = x relative to the function. Inverse proportionality, however, yields a reciprocal relation graphically. Why do these two things have similar names yet mean different things? Inverse Functions One-Way Only Are there two functions, f and g, such that (f of g)(x) = x but (g of f)(x) does not equal x? Domain and Range of an Inverse Function Why is the domain of a function equal to the range of the inverse function? Inverse Functions - Which Statement is True? Does (f o g)^(-1) equal f^(-1) o g^(-1) or g^(-1) o f^(-1)? How can you prove it? Inverse of a Multivariate Function Let f:NxN -> N such that f(x,y) = 2^x(2y + 1) - 1 for all natural numbers x, y. Let the inverse of f, g be given by g:N -> NxN. Find the inverse of the function g.
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