[Answer] Which represents the inverse of the function f(x) = 4x?

Answer: h(x) = x

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Which represents the inverse of the function f(x) = 4x? Single-variable calculus is primarily concerned with functions that map real numbers to real numbers. Such functions are often defined through formulas such as: ${\displaystyle f(x)=(2x+8)^{3}.}$ A surjective function f from the real numbers to the real numbers possesses an inverse as long as it is one-to-one. That is the graph of y = f(x) has for each possible y value only one corresponding x value and thus passes the horizontal line test. Single-variable calculus is primarily concerned with functions that map real numbers to real numbers. Such functions are often defined through formulas such as: ${\displaystyle f(x)=(2x+8)^{3}.}$ A surjective function f from the real numbers to the real numbers possesses an inverse as long as it is one-to-one. That is the graph of y = f(x) has for each possible y value only one corresponding x value and thus passes the horizontal line test. The following table shows several standard functions and their inverses: Function f(x) Inverse f (y) Notes x + a y − a a − x a − y mx y/m m ≠ 0 1/x (i.e. x ) 1/y (i.e. y ) x y ≠ 0 x √y (i.e. y ) x y ≥ 0 only x √y (i.e. y ) no restriction on x and y x √y (i.e. y ) x y ≥ 0 if p is even; integer p > 0 2 lb y y > 0 e ln y y > 0 10 log y y > 0 a loga y y > 0 and a > 0 trigonometric functions inverse trigonometric functions various restrictions (see table below) hyperbolic functions inverse hyperbolic functions various restrictions One approach to finding a formula for f if it exists is to solve the equation y = f(x) for x. For example if f is the function ${\displaystyle f(x)=(2x+8)^{3}}$ then we must solve the equation y = (2x + 8) for x: ${\displaystyle {\begin{aligned}y&=(2x+8)^{3}\\{\sqrt[{3}]{y}}&=2x+8\\{\sqrt[{3}]{y}}-8&=2x\\{\dfrac {{\sqrt[{3}]{y}}-8}{2}}&=x.\end{aligned}}}$ Thus the inverse function f is given by the formula ${\displaystyle f^{-1}(y)={\frac {{\sqrt[{3}]{y}}-8}{2}}.}$ Wed Feb 19 2003 13:30:00 GMT-0500 (Eastern Standard Time) · Intuitively a function is a process that associates each element of a set X to a single element of a set Y.. Formally a function f from a set X to a set Y is defined by a set G of ordered pairs ( x y) such that x ∈ X y ∈ Y and every element of X is the first component of exactly one ordered pair in G. In other words for every x in X there is exactly one element y … In mathematics the logarithm is the inverse function to exponentiation.That means the logarithm of a given number x is the exponent to which another fixed number the base b must be raised to produce that number x .In the simplest case the logarithm counts the number of occurrences of the same factor in repeated multiplication; e.g. sinc...

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