Which of the following pairs of functions are | vedclass

Name: Exam Paper Generator | JEE NEET Paper Generator | Vedclass
Brand: Vedclass
Rating: 5 (35 reviews)

Question

(D) Let us analyze each pair:$1$. For option $A$: $g(x) = \cot^2 x - \cos^2 x = \frac{\cos^2 x}{\sin^2 x} - \cos^2 x = \cos^2 x \left( \frac{1}{\sin^2

Vedclass · Accepted Answer

All of the above

Vedclass · Answer

(D) Let us analyze each pair:$1$. For option $A$: $g(x) = \cot^2 x - \cos^2 x = \frac{\cos^2 x}{\sin^2 x} - \cos^2 x = \cos^2 x \left( \frac{1}{\sin^2 x} - 1 ight) = \cos^2 x \left( \frac{1 - \sin^2 x}{\sin^2 x} ight) = \cos^2 x \cdot \frac{\cos^2 x}{\sin^2 x} = \cos^2 x \cdot \cot^2 x = f(x)$. Since the domains are also identical $(x 
eq n\pi)$,these functions are identical.$2$. For option $B$: $f(x) = 	an(	an^{-1} x) = x$ for all $x \in \mathbb{R}$. $g(x) = \cot(\cot^{-1} x) = x$ for all $x \in \mathbb{R}$. Since both functions are $y = x$ for all $x \in \mathbb{R}$,they are identical.$3$. For option $C$: $f(x) = 	ext{sgn}(x)$. $g(x) = 	ext{sgn}(	ext{sgn}(x))$. If $x > 0$,$f(x) = 1$ and $g(x) = 	ext{sgn}(1) = 1$. If $x = 0$,$f(x) = 0$ and $g(x) = 	ext{sgn}(0) = 0$. If $x Since all pairs are identical,the correct option is $D$.

Which of the following pairs of functions are identical?

Similar Questions

If the set of all values of $a$ is $[\alpha, \beta] \cup [\gamma, \delta]$ for which the function $f(x) = \begin{cases} 3x + |a^2 - 4|; & a \leqslant x < 1 \\ 5 - x^2; & x \geqslant 1 \end{cases}$ has its largest value at $x = 1$,then find the value of $(\alpha + \beta + \gamma + \delta)$.

If $f(x) = \cos (\log x)$,then $f(x^2)f(y^2) - \frac{1}{2}\left[ f\left( \frac{x^2}{y^2} \right) + f(x^2y^2) \right]$ has the value

Consider the function $f(x) = x^3 - 8x^2 + 20x - 13$. The number of positive integers $x$ for which $f(x)$ is a prime number is:

$f: R \rightarrow R$ is a function defined by $f(x) = \frac{1}{e^x + 2e^{-x}}$. Assertion $(A): f(c) = \frac{1}{3}$ for some values of $c \in R$. Reason $(R): 0 < f(x) \leq \frac{1}{2\sqrt{2}}$ for all $x \in R$. Then which of the following options is correct?

The function $f(x) = [|x|] - |[x]|$ where $[x]$ denotes the greatest integer function:

Vedclass Test Series

Exam Paper Generator

Online Exam Module