Home
Class 12
MATHS
Let f(x): R^+ to R^+ is an invertible ...

Let `f(x): R^+ to R^+` is an invertible function such that `f^(prime)(x)>0a n df"(x)>0AAx in [1,5]dot` If `f(1)=1` and `f(5)=5` and area under the curve `y=f(x)` on x-axis from `x=1tox=5i s8` sq. units, then area bounded by `y=f^(-1)(x)` on x-axis from `x=1tox=5` is

A

12

B

16

C

18

D

20

Text Solution

Verified by Experts

The correct Answer is:
B
Promotional Banner

Topper's Solved these Questions

  • AREA UNDER CURVES

    VK JAISWAL ENGLISH|Exercise EXERCISE (ONE OR MORE THAN ONE ANSWER IS/ARE CORRECT)|4 Videos

  • AREA UNDER CURVES

    VK JAISWAL ENGLISH|Exercise EXERCISE (COMPREHENSION TYPE PROBLEMS)|6 Videos

  • APPLICATION OF DERIVATIVES

    VK JAISWAL ENGLISH|Exercise EXERCISE (SUBJECTIVE TYPE PROBLEMS)|22 Videos

  • BIONMIAL THEOREM

    VK JAISWAL ENGLISH|Exercise Exercise-4 : Subjective Type Problems|16 Videos

Similar Questions

Explore conceptually related problems

Let f(x) = minimum (x+1, sqrt(1-x))" for all "x le 1. Then the area bounded by y=f(x) and the x-axis is

If f: R->R is an odd function such that f(1+x)=1+f(x) and x^2f(1/x)=f(x),x!=0 then find f(x)dot

If f:R rarr R is a function such that f(5x)+f(5x+1)+f(5x+2)=0, AA x in R , then the period of f(x) is

f:[0,5]rarrR,y=f(x) such that f''(x)=f''(5-x)AAx in [0,5] f'(0)=1 and f'(5)=7 , then the value of int_(1)^(4)f'(x)dx is

The area (in sq. units) bounded by the curve f(x)=max(|x|-1, 1-|x|) with the x- axis from x=-1 " to " x =1 is

Let f(x) be a function such that 2f(x)+f((x+1)/(x-1))=x. AAx in R-{1}dot If 3f(x)+f((x+1)/(x-1))=lambdax. AAx in R-{1}, then value of lambda is

If f: R to R is defined as f(x)=2x+5 and it is invertible , then f^(-1) (x) is

Let f(x)=min(x+1,sqrt(1-x))AA x le 1 . Then, the area (in sq. units( bounded by y=f(x), y=0 and x=0 from y=0 to x=1 is equal to

Let f(x)= minimum {e^(x),3//2,1+e^(-x)},0lexle1 . Find the area bounded by y=f(x) , X-axis and the line x=1.

Let f(x) is a differentiable function on x in R , such that f(x+y)=f(x)f(y) for all x, y in R where f(0) ne 0 . If f(5)=10, f'(0)=0 , then the value of f'(5) is equal to