Home
Class 11
MATHS
If f(x)=e^(x) and g(x)=log(e)x, then sho...

If `f(x)=e^(x) and g(x)=log_(e)x,` then show that `"fog=gof"` and find `f^(-1) and g^(-1)`.

Text Solution

Verified by Experts

The correct Answer is:
`e ^(x)`
Doubtnut Promotions Banner Mobile Dark
|

Topper's Solved these Questions

  • FUNCTIONS

    VIKRAM PUBLICATION ( ANDHRA PUBLICATION)|Exercise TEXTUAL EXERCISES (EXERCISE-1 (C)|34 Videos

  • FUNCTIONS

    VIKRAM PUBLICATION ( ANDHRA PUBLICATION)|Exercise TEXTUAL EXERCISES (EXERCISE-1 (A) |24 Videos

  • DIRECTION COSINES AND DIRECTION RATIOS

    VIKRAM PUBLICATION ( ANDHRA PUBLICATION)|Exercise TEXTUAL EXERCISE -6(B)|21 Videos

  • HYPERBOLIC FUNCTIONS

    VIKRAM PUBLICATION ( ANDHRA PUBLICATION)|Exercise EXERCISE - 9(a)|10 Videos

Similar Questions

Explore conceptually related problems

If f(x) = sinx, g(x) =2x and h(x)= cos x then show that fog = go(fh).

If f(x)=sqrt(x^(3)-1) and g(x)=root(3)(x^(2)+1) , then (fog)(x)=

Knowledge Check

  • If f(x)=(1-x)^(1//2) and g(x)=ln(x) then the domain of (gof)(x) is

    A
    `(-oo, 2)`
    B
    `(-1, 1)`
    C
    `(-oo, 1]`
    D
    `(-oo, 1)`

  • Let f(x)=sin x and g(x)= log_(e)|x| . If the ranges of the composition functions fog and gof are R_(1) and R_(2) , respectively, then

    A
    `R_(1)={u: -1 le u lt 1}, { v: -oo v lt 0}`
    B
    `R_(1)={u : - oo lt u lt 0}, R_(2)={v: -oo lt v lt0}`
    C
    `R_(1)={u: -1 lt u lt 1},R_(2)= { v: oo lt v lt 0}`
    D
    `R_(1)={u : -1 le u le 1}, R_(2)={v: -oo lt v lt 0}`

  • If f(x)=|log_e(x||, then f'(x) equals.

    A
    `1/(|x|)`, where `x != 0`
    B
    `1/x"for"|x|gt1and-1/x"for"|x|lt1`
    C
    `-1/x"for"|x|gt1and-1/x"for"|x|lt1`
    D
    `1/x"for"|x|gt0and-1/x"for"|x|lt1`

    • Similar Questions

    Explore conceptually related problems

    If the function f(x) = x^3 + e^(x/2) and g(x) =f^-1(x) , then the value of g'(1) is

    Let f(x) = x^(2), g(x) = 2^(x) . Then solve the equation (fog)(x)=(gof)(x) .

    Let f (x) = x ^(2), g (x) = 2 ^(x). Then solve the equation (fog) (x) = (gof) (x)

    Let f(x) = sinx and g(x) = log|x| .If the ranges of composite functions fog and gof are R_1 and R_2 repsectively, then

    If f(x) = log_(x)(lnx) then f'(x) at x = e is

    Home
    Profile