Question:
Domain of the function $f (x) = \log_x \; \cos \; x$, is
Domain of the function $f (x) = \log_x \; \cos \; x$, is
Updated On: Sep 3, 2024
- $\left( - \frac{\pi}{2} , \frac{\pi}{2}\right) - \left\{1\right\} $
- $\left[ - \frac{\pi}{2} , \frac{\pi}{2}\right] - \left\{1\right\} $
- $\left( - \frac{\pi}{2} , \frac{\pi}{2}\right) $
- $None\, of\, these$
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The Correct Option is D
Solution and Explanation
We have the function
$f(x)=\log _{x} \cos x$
$f(x)$ is defined for $\cos x>0$,
$x >0, x \neq 1$
$\because \cos x >0$
$\Rightarrow -\frac{\pi}{2} < x < \frac{\pi}{2}$
Also, $x > 0, x \neq 1$
$\therefore$ Domain of $f$ is $\left(0, \frac{\pi}{2}\right)-\{1\}$.
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Concepts Used:
Relations and functions
A relation R from a non-empty set B is a subset of the cartesian product A × B. The subset is derived by describing a relationship between the first element and the second element of the ordered pairs in A × B.
A relation f from a set A to a set B is said to be a function if every element of set A has one and only one image in set B. In other words, no two distinct elements of B have the same pre-image.
Representation of Relation and Function
Relations and functions can be represented in different forms such as arrow representation, algebraic form, set-builder form, graphically, roster form, and tabular form. Define a function f: A = {1, 2, 3} → B = {1, 4, 9} such that f(1) = 1, f(2) = 4, f(3) = 9. Now, represent this function in different forms.
- Set-builder form - {(x, y): f(x) = y2, x ∈ A, y ∈ B}
- Roster form - {(1, 1), (2, 4), (3, 9)}
- Arrow Representation
