The number of integers in the domain of f ( x )=(1/√ ln ( cos -1 x )), is

Question

The number of integers in the domain of f ( x )=(1/√ ln ( cos -1 x )), is (A) 2 (B) 3 (C) 4 (D) 6

Tardigrade Admin · Accepted Answer

We have f(x)=(1/√ ln cos -1 x) For domain of f ( x ), ln ( cos -1 x )>0 ⇒ cos -1 x >1 and cos -1 x ≤ π ⇒ cos π ≤ x ≤ cos 1 ⇒-1 ≤ x< cos 1. Hence number of integers in the domain of f ( x ) are 2 i.e., -1 and 0 .

Q. The number of integers in the domain of $f (x) = \frac{1}{l n ( c o s ^{- 1} x )}$ , is

2

3

4

6

We have $f (x) = \frac{1}{l n c o s ^{- 1} x}$
For domain of $f (x), ln (cos^{- 1} x) > 0 \Rightarrow cos^{- 1} x > 1$ and $cos^{- 1} x \leq π$ $\Rightarrow cos π \leq x \leq cos 1 \Rightarrow - 1 \leq x < cos 1$ .
Hence number of integers in the domain of $f (x)$ are 2 i.e., -1 and 0 .

Q. The number of integers in the domain of f(x)=ln(cos−1x)​1​, is

2

3

4

6

We have f(x)=lncos−1x​1​ For domain of f(x),ln(cos−1x)>0⇒cos−1x>1 and cos−1x≤π ⇒cosπ≤x≤cos1⇒−1≤x<cos1. Hence number of integers in the domain of f(x) are 2 i.e., -1 and 0 .

Q. The number of integers in the domain of $f (x) = \frac{1}{l n ( c o s ^{- 1} x )}$ , is

We have $f (x) = \frac{1}{l n c o s ^{- 1} x}$
For domain of $f (x), ln (cos^{- 1} x) > 0 \Rightarrow cos^{- 1} x > 1$ and $cos^{- 1} x \leq π$ $\Rightarrow cos π \leq x \leq cos 1 \Rightarrow - 1 \leq x < cos 1$ .
Hence number of integers in the domain of $f (x)$ are 2 i.e., -1 and 0 .