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Prove that the function f: N to Y define...

Prove that the function `f: N to Y` defined by `f(x) = x^(2)`, where `y = {y : y = x^(2) , x in N}` is invertible. Also write the inverse of f(x).

Text Solution

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The correct Answer is:
f is invertible with `f^(-1) = g`
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Verify whether the function f : N to Y defined by f(x) = 4x + 3 , where Y = {y : y = 4x + 3, x in N} is invertible or not. Write the inverse of f(x) if exists.

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Knowledge Check

  • The function f(x) is defined by f(x) = (x+2)e^(-x) is

    A
    A. decreasing for all x
    B
    B. decreasing in `(-oo, -1)` and increasing in `(-1, oo))`
    C
    C. increasing for all x
    D
    D. decreasing in `(-1,oo)` and increasing in `(-oo, -1)`

  • Let f: N rarr N be defined by f(x)=x^(2)+x+1 then f is

    A
    one-one, onto
    B
    many one onto
    C
    one-one but not onto
    D
    onto but not one-one

  • The function defined by y = x^(2) is

    A
    increasing for ` x lt 0`
    B
    decreasing for `x gt 0`
    C
    maximum at x = 0
    D
    minimum at x =0

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