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If f(x)=(3x-7)/(5x-3) then (fof)(x)=...

If `f(x)=(3x-7)/(5x-3)` then `(fof)(x)=`

A

`x`

B

`-x`

C

`3x`

D

`f(x)`

Text Solution

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The correct Answer is:
A
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Show that if f :R {(7)/(5)} to R - {(3)/(5)} is defined by f (x) = (3x +4)/( 5x -7) and g :R - {(3/(5)} to R - {(7)/(5)} is defined by g (x) = (7x +4)/(5x -3), then fog = I _(A) and gof =I _(B), where, A = R - {(3)/(5)}, B+R -{(7)/(5)},I_(A)(x) =x, AA x in A, I_(B)|(x) =x , AA x in B are called identity functions on sets A and B, respectively.

Find f(x)=7^(3+3x)(x gt0) , then find f'(x) .

Knowledge Check

  • If f(x) = (3x+2)/(5x-3) , then

    A
    `f^(-1)(x) =f(x) `
    B
    `f^(-1)(x) =-f(x)`
    C
    `f^(-1)(x) = -1/19 f(x)`
    D
    `(fof)(x) =-x`

  • If f(x) =(10-x^(7))^(1//7) , then fof(x)=

    A
    10
    B
    x
    C
    `x^(7)`
    D
    `10^(7)`

  • If f(x)=3x-5 , then f^(-1)(x)

    A
    is given by `(1)/((3x-5))`
    B
    is given by `((x+5))/(3)`
    C
    does not exist because f is not one-one
    D
    does not exist because f is not onto

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    If f : R to R be given by f (x) = (3 -x ^(3)) ^(1/3), then fof (x) is

    If f(x)=(4-(x-7)^(3))^(1/5) , then f^(-1)(x)=

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