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Let f: NvecR be a function defined as f(...

Let `f: NvecR` be a function defined as `f(x)=4x^2+12 x+15.` Show that `f: NvecS ,` where `S` is the range of `f,` is invertible. Also find the inverse of `f`

Text Solution

Verified by Experts

The correct Answer is:
`f^(-1) = (sqrt(x-6) -3)/( 2)`.
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Let f: N to R be defined by f(x) = 4x^(2) + 12x+ 15 . Show that f: N to S where S is the range of function f, is invertible. Also find the inverse of f.

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Knowledge Check

  • Let f : R rarr R be a function defined by f(x) = x^3 + 5 . Then f^-1(x) is

    A
    `(x+5)^(1/3)`
    B
    `(x-5)^(1/3)`
    C
    `(5-x)^(1/3)`
    D
    5-x

  • Let f:RtoR be a function defined by : f(x)=(x^(2)+2x+5)/(x^(2)+x+1) is :

    A
    one-one and into
    B
    one-one and onto
    C
    many-one and onto
    D
    many-one and into

  • Let f:NtoY be a function defined as f(x)=4x+3 , where Y={yinN,y=4x+3 for some x inN }. Show that f is invertible and its inverse is :

    A
    `g(y)=(y-3)/(4)`
    B
    `g(y)=(3y+4)/(3)`
    C
    `g(y)=4+(y+3)/(4)`
    D
    `g(y)=(y+3)/(4)`

    • Similar Questions

    Explore conceptually related problems

    Let f : N to R be defined by f(x) = 4x^(2) + 12x + 15 , show that f: N to S , where S is the function, is invertible. Also find the inverse.

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

    Let f : R to R be a function defined by f(x) = 4x - 3 AA x in R . Then Write f^(-1) .

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

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