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3 July, 10:36

What is the inverse of the fuction f (x) = x+3

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  1. 3 July, 10:41
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    Inverse of function f (x) is y = x-3

    Step-by-step explanation:

    Given:

    f (x) = (x+3)

    To Find:

    Inverse of f (x)

    Solution:

    Inverse of the function:

    Let f: X - > Y be a function with domain X and target set Y. Then g is the inverse of f if g is a function with domain Y and target set X such that

    g (f (x)) = x for all x in X

    f (g (y)) = y for all y in Y.

    f has an inverse function if and only if f is both one-to-one and onto. If f is one-to-one and onto, then its inverse function g is defined implicitly by the relation g (f (x)) = x.

    To find the inverse function, swap x and y, and solve the resulting equation for x.

    If the initial function is not one-to-one, then there will be more than one inverse.

    Let y = f (x) = x+3

    So, swapping the variables: y=x+3 becomes x=y+3

    Now, solve the equation x=y+3 for y.

    y=x-3

    y=x-3
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