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Let R+ be the set of all non-negative re...

Let R+ be the set of all non-negative real numbers. Show that the function `f : R+ rarr [ 4 ,oo ]` given by `f(x) = x^(2) + 4` is invertible and write the inverse of f.

Text Solution

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The correct Answer is:
`f^(-1) = sqrt(y-4)`
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Let R_(+) be the set of all non-negative real numbers. Show that the function f: R_(+) to [4,oo] defind by f(x) = x^(2)+4 Is invertible and write the inverse of f.

Let R+ be the set of all non negative real numbers. Show that the function f: R_(+) to [4, infty] given by f(x) = x^2 + 4 is invertible and write inverse of 'f'.

Knowledge Check

  • The function f : R rarr R given by f(x) = 5-3 sin x

    A
    only one-one
    B
    only onto
    C
    both one-one and onto
    D
    neither one-one nor onto

  • If the function f : R rarr A given by f(x) = (x^2)/(x^2+1) is a surjective then A =

    A
    R
    B
    [0, 1]
    C
    (0, 1]
    D
    [0, 1)

    • Similar Questions

    Explore conceptually related problems

    Let R+ be the set of all non-negative real number. Show that the faction f : R, to [4, oo) defined f(x) = x^(2) + 4 is invertible. Also write the inverse of f.

    Show that the function f: R rarr R given by f(x) = 4x + 3 is invertible. Find the inverse of f.

    Show that the function f: R to R given by f (x) = x ^(3) is injective.

    If R, is the set of all non-negative real numbers prove that the f : R, to [-5, oo) defined by f(x) = 9x^(2) + 6x - 5 is invertible. Write also f^(-1)(x) .

    If R, is the set of all non - negative real numbers prove that the function f:R_(+) to [-5, infty]" defined by "f(x)=9x^(2)+6x-5 is invertible. Write also f^(-1)(x) .

    Prove that the function f: R to R defined by f(x) = 4x + 3 is invertible and find the inverse of 'f' .

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