# learning journal unit4.docx - An inverse function does the...

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An inverse function does the exact opposite, undoing what the original functiondoes. It is usually denoted asf-1(x),and it reverses thef(x)processes. Before a functioncan have an inverse, it must first be one-to-one; that is, it must pass the horizontal linetest, which verifies whether a function is one-to-one by intersecting the function's graphonly at one point. The graph off-1(x)on a set of axes can be obtained by reflecting ouroriginal function on a diagonal liney = xwhich is called identity line (Abramson, 2017, p.262). Importantly, one must note that not all functions have an inverse function.The functionf(x)can be reversed in such a way that the input of the function becomesthe output and the output becomes an input, and the resulting reversed relationship isitself a functionf-1(x), thenf-1(x)is the inverse off(x).The definition of the inverse of a function state that, the domain off(x)is equal to the rangeoff-1(x)and vice versa. This means that, if the functionf(x) is the set of ordered pairs (x, y),then the inverse off(x)is the set of ordered pairs(y, x)and when the function is defined by an

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Term
Spring
Professor
N/A
Tags
Inverse function, Abramson