MTH 162 Study Guide - Final Guide: Improper Integral, Trapezoidal Rule, Hyperbolic Function
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Provide a generalization to each of the key terms listed in this section. Domain and range f "s domain=f 1"s range f " :range=f 1"s domain f and f 1 x f (x) f 1 (f (x)) = x. Domain of f : f 1 (f (x)) = x x f 1 (x) f(cid:0)f 1 (x)(cid:1) = x. Domain of f 1 : f(cid:0)f 1 (x)(cid:1) = x. A function"s graph, f , and f 1, which is its inverse, are fully symmetric, but with respect to the line, which is y = x. Since y = f (x), interchange both x and y, which are the variables, to create x = f (y), which implies f 1, which would be the inverse function, implicitly. Solve the implicit equation for y, which would be in terms of x in order to obtain f 1"s explicit form (if possible).
