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f : R to R be defined as f(x) = 4x + 5 A...

`f : R to R` be defined as `f(x) = 4x + 5 AA x in R` show that f is invertible and find `f^(-1)`.

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Knowledge Check

  • Let f:R to R be defined by f(x) = 1/x AA x in R , then f is ________

    A
    onto
    B
    not defined
    C
    one - one
    D
    bijective

  • Let f: R to R be defined by f(x) = x^(4) , then

    A
    f is one-one but not onto
    B
    f is neither one-one nor onto
    C
    f is one-one and onto
    D
    f may be one-one and onto

  • Let f : R to R be defined by f(x)=x^(4) , then

    A
    1.f is one - one and onto
    B
    2.f may be one - one and onto
    C
    3.f is one - one but not onto
    D
    4.f is neither one - one nor onto

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    Explore conceptually related problems

    Let A= R- (3), B= R-{1} . Let f: A to B be defined by f(x)= ((x-2)/(x-3)) AA x in A . Then show that f is bijective. Hence find f^(-1) (x) .

    If f:ArarrA defined by f(x)=(4x+3)/(6x-4) where A=R-{2/3} , show that f is invertible and f^(-1)=f .

    If f : R to R defined by f(x) = 1+x^(2), then show that f is neither 1-1 nor onto.

    Let f: R rarr R be defined by f(x)= (1)/(x) AA x inR , then f is _______

    If : R to R defined by f(x) = x^5 + 1 and if fog(x) =x then g(x) is given by

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