What is the inverse of the function f(x) = x + 12?
The inverse of adding 12 is subtracting 12, so the inverse function is g(x) = x -12.
(There is a special method for finding the inverse of more complicated functions, but it isn't needed here.)
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In order for a fourth degree function to have an inverse function, its domain must be restricted. Otherwise the inverse function will not pass the vertical-line test.Ex.f(x) = x^4 (x>0), the original functionf-1(x) = x ^ (1/4), the inverse
XX or X*X, can be written as X squared. The inverse of a function "sort of cancels it out". I know the inverse of a square is the square root. Since we need the inverse of X squared, it's inverse is the square root of X. sqrt(x)
The logarithm function. If y = bx, then x = by is the inverse --> y = logb(x). If b = 10, then the function is often stated with the '10' implied: just log(x). For natural logarithms (y = ex), the function y = ln(x) [which indicates loge(x)] is the inverse.
An exponential function is of the form y = a^x, where a is a constant. The inverse of this is x = a^y --> y = ln(x)/ln(a), where ln() means the natural log.