IIT JEE , AIEEE Forum - Mathematics , Differential Calculus

ishita247

The domain of

f(x)=cos^-1{(1+x²)/2x} +

sin(cos x) is

a) R-{0}

b) (0,1)

c) (-1,1)

d) {-1,1}

anchal_1991

is it a.
pls tell i wil try to explain

akhil_o

d)?

cos inverse is definerd only from -1 to 1
so 1+X²/2x<=1
1+x²<=2x
(1-x)²<=0

since LHS is positive
only =0 works
so
(1-x)²=0
1-x=0
x=1

also
1+X²/2x>=-1
similarly we get x=-1

so only possible values satisfy the function domain s -1,1

also we have that second part is satisfied by -1 and 1

so d

ayshwarya

wats d ansr yaar plz tell

anchal_1991

bt wat abt x=0
it is also not defined at it

akhil_o

precisely ...thats why the ONLY solutions are -1 and 1

ishita247

thnxx d ans is d) indeed

anchal_1991

ok thanx
so dat option means it has jst 2 values in it

ishita247

yup

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