###### Answer: B. f(x) is a one-to-one function.

The function f : R → R defined by f ( x ) = 2x + 1 is surjective (and even bijective) because for every real number y we have an x such that f ( x ) = y: such an appropriate x is (y − 1)/2. The function f : R → R defined by f ( x ) = x 3 − 3x is surjective because the pre-image of any real number y is the solution set of the cubic polynomial …

A proof that a function f is injective depends on how the function is presented and what properties the function holds. For functions that are given by some formula there is a basic idea. We use the definition of injectivity namely that if f ( x ) = f (y) then x = y. Here is an example: f = 2x + 3 . Proof: Let f : X → Y. Suppose f ( x ) = f (y).

Sun May 18 2003 14:30:00 GMT-0400 (Eastern Daylight Time) · The notation f −1 is sometimes also used for the inverse function of the function f which is not in general equal to the multiplicative inverse . For example the multiplicative inverse 1/(sin x ) = (sin x ) −1 is the cosecant of x and not the inverse sine of x denoted by sin −1 x or arcsin x . Only for linear maps are they strongly related …

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Injective function – Wikipedia

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Injective function – Wikipedia

In mathematics function composition is an operation that takes two functions f and g and produces a function h such that h( x ) = g( f ( x )).In this operation the function g is applied to the result of applying the function f to x .That is the functions f : X → Y and g : Y → Z are composed to yield a function that maps x in X to g( f ( x )) in Z.. Intuitively if z is a function of y and y is a …

Examples Inverse functions. A common type of implicit function is an inverse function .Not all functions have a unique inverse function . If g is a function of x that has a unique inverse then the inverse function …