JEE MATHEMATICS MCQ: FUNCTIONS

1 Medium

1 of 1

Application +4 | -1

Let

f: \mathbb{R}-\{0\} \rightarrow \mathbb{R}

be a function satisfying

f\left(\frac{x}{y}\right)=\frac{f(x)}{f(y)}

for all

x, y, f(y) \neq 0

. If

f^{\prime}(1)=2024

, then

View answer and explanation

Correct option: A

x f^{\prime}(x)-2024 f(x)=0

The correct answer is A (

x f^{\prime}(x)-2024 f(x)=0

) because by using the given functional equation and differentiation, we can derive the relationship between f(x) and its derivative.

More Questions from FUNCTIONS

Practice All Chapter MCQs →

f:(-\infty, 2] \longrightarrow(-\infty, 4]

f(x)=x(4-x)

f^{-1}(x)

g(f(x))=|\sin x|

f(g(x))=(\sin \sqrt{x})^2

f:\left( {2,\;3} \right) \to \left( {0,\;1} \right)

f\left( x \right) = x - \left[ x \right]

{f^{ - 1}}\left( x \right)

f: R \rightarrow R

f(x)=x^4

f(x)=(x+1)^2-1(x \geq-1)

S=\left\{x: f(x)=f^{-1}(x)\right\}