Home
Class 12
MATHS
If f :R ->R , f(x)=x^3 +3,and g:R->R,g(x...

If `f :R ->R` , `f(x)=x^3 +3`,and `g:R->R`,`g(x)=2x + 1`, then `f^(-1)(g^(-1)(23))` equals

A

2

B

3

C

`(14)^(1//3)`

D

`(15)^(1//3)`

Text Solution

Verified by Experts

The correct Answer is:
A
`f^(-1)og^(-1)(23)=(gof)^(-1)(23)`
`"Now "gof(x)=2(x^(3)+3)+1`
`"For "2(x^(3)+3)+1=23`
`rArr" "x=2`
`therefore" "gof^(-1)(23)=2`
Promotional Banner

Topper's Solved these Questions

  • FUNCTIONS

    CENGAGE PUBLICATION|Exercise Multiple Correct Answers Type|9 Videos

  • FUNCTIONS

    CENGAGE PUBLICATION|Exercise Comprehension Type|7 Videos

  • EQUATION OF PLANE AND ITS APPLICATIONS -II

    CENGAGE PUBLICATION|Exercise DPP 3.4|8 Videos

  • GETTING STARTED WITH GRAPHS

    CENGAGE PUBLICATION|Exercise Exercises 1.18|1 Videos

Similar Questions

Explore conceptually related problems

Let f:R→R: f(x)=x+1 and g:R→R: g(x)=2x−3 . Find (f−g)(x) .

Let f:R to R and g:R to R is define by f(x)=2x+3 and g(x)=3x-2 , then find (f circ g)^(-1)(x)

Let f:R to R and g:R to R is define by f(x)=2x+3 and g(x)=3x-2 , then find (g circ f)^(-1)(x)

Let f:R to R be defined by f(x)=x^(2) and g:R to R be defined by g(x)=x+5 . Then , (gof)(x) is equal to -

If f: R^+ to R , f(x) + 3x f(1/x)= 2(x+1),t h e n find f(x)

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

If the function f: R to R is defined by f(x)=x^(2)-6x-14 , then f^(-1)(2) is equal to -

f(x) and g(x) are two differentiable functions on [0, 2] such that f''(x)-g''(x)=0, f'(1)=2, g'(1)=4, f(2)=3 and g(2)=9 , then [f(x)-g(x)] at x=(3)/(2) is equal to -

If f(x)=3x+1,g(x)=x^3+2 , then (f+g)/(fg) (0) =?

Let f:R to R and g:R to R is define by f(x)=2x+3 and g(x)=3x-2 , then find (f circ g)(-1)