Home
Class 12
MATHS
f(x)=sin^-1x +|sin^-1x| +sin^-1|x| no. ...

`f(x)=sin^-1x +|sin^-1x| +sin^-1|x| ` no. of solution of equation f(x)=x is

A

1

B

0

C

2

D

3

Text Solution

Verified by Experts

The correct Answer is:
A
`f(x)={{:(3sin^(-1)x,,x in[0,1]),(-sin^(-1)x,,x in[-1,0)):}`
The graph of the function y = f(x) is an shown in the following figure

From the graph f(x) = x has only one solution, x = 0
Range of y = f(x) is `[0, 3pi//2]`
For f(x) = k having two solutions, `k in (0, pi//2]`
Promotional Banner

Similar Questions

Explore conceptually related problems

f(x)=sin^(-1)x+|sin^(-1)x|+sin^(-1)|x| no.of solution of equation f(x)=x is

Let f(x)=sin^(-1)x+|sin^(-1)x|+sin^(-1)|x| If the equation f(x) = k has two solutions, then true set of values of k is

Let f(x)=sin^(-1)x+|sin^(-1)x|+sin^(-1)|x| The range of f(x) is

If f(x)=-x+sin x, then the number of solution(s) of the equation f^(-1)(x)=5, is

Consider a real-valued function f(x)= sqrt(sin^-1 x + 2) + sqrt(1 – sin^-1x) then The domain of definition of f(x) is

If f(x)=2+|sin^(-1)x| , it is

f(x)= sin^(-1)((x)/(1+|x|))

Let alpha is the solution of equation sin^(-1)(2sin^(-1)(cos^(-1)(tan^(-1)x)))=0 and beta is the solution of equation sin^(-1)x+sin^(-1)x^(2)=(pi)/(2), then -