Let f be a function satisfying f(xy) = frac{f | vedclass

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

Question

(A) Given the functional equation $f(xy) = \frac{f(x)}{y}$.First,we find the value of $f(1)$ by setting $x=1$ and $y=1$:$f(1) = \frac{f(1)}{1} \implie

Vedclass · Accepted Answer

$15$

Vedclass · Answer

(A) Given the functional equation $f(xy) = \frac{f(x)}{y}$.First,we find the value of $f(1)$ by setting $x=1$ and $y=1$:$f(1) = \frac{f(1)}{1} \implies f(1) = f(1)$.Setting $x=1$ in the original equation gives $f(y) = \frac{f(1)}{y}$.Let $f(1) = c$,then $f(y) = \frac{c}{y}$.We are given $f(30) = 20$,so:$20 = \frac{c}{30} \implies c = 600$.Thus,the function is $f(x) = \frac{600}{x}$.Now,we calculate $f(40)$:$f(40) = \frac{600}{40} = 15$.

Let $f$ be a function satisfying $f(xy) = \frac{f(x)}{y}$ for all positive real numbers $x$ and $y.$ If $f(30) = 20,$ then the value of $f(40)$ is-

Similar Questions

The number of real linear functions $f(x)$ satisfying $f(f(x))=x+f(x)$ is

If $f(a) = a^2 + a + 1$,then the number of solutions of the equation $f(a^2) = 3f(a)$ is:

Let $f : R - \{0, 1\} \rightarrow R$ be a function such that $f(x) + f\left(\frac{1}{1-x}\right) = 1 + x$. Then $f(2)$ is equal to:

The function $t$ which maps temperature in degree Celsius into temperature in degree Fahrenheit is defined by $t(C) = \frac{9C}{5} + 32$. Find $t(28)$.

If $f(x + ay, x - ay) = axy$,then $f(x, y)$ is equal to

Vedclass Test Series

Exam Paper Generator

Online Exam Module