Domain of the function f (x) = logx cos x, is

Question

Domain of the function f (x) = logx cos x, is (A) ( - (π/2) , (π/2)) - 1  (B) [ - (π/2) , (π/2)] - 1  (C) ( - (π/2) , (π/2))  (D) None of these

Tardigrade Admin · Accepted Answer

We have the function f(x)= log x cos x f(x) is defined for cos x>0, x >0, x ≠ 1 ∵ cos x >0 ⇒ -(π/2) < x < (π/2) Also, x > 0, x ≠ 1 ∴ Domain of f is (0, (π/2))- 1 .

Q. Domain of the function $f (x) = lo g_{x} cos x$ , is

$(- \frac{π}{2}, \frac{π}{2}) - {1}$

$[- \frac{π}{2}, \frac{π}{2}] - {1}$

$(- \frac{π}{2}, \frac{π}{2})$

$N o n e o f t h ese$

We have the function
$f (x) = lo g_{x} cos x$
$f (x)$ is defined for $cos x > 0$ ,
$x > 0, x \neq = 1$
$∵ cos x > 0$
$\Rightarrow - \frac{π}{2} < x < \frac{π}{2}$
Also, $x > 0, x \neq = 1$
$∴$ Domain of $f$ is $(0, \frac{π}{2}) - {1}$ .

Q. Domain of the function f(x)=logx​cosx, is

(−2π​,2π​)−{1}

[−2π​,2π​]−{1}

(−2π​,2π​)

Noneofthese