A function \( f: \mathrm{R} \rightarrow \mathrm{R} \) is defined by \[ \begin{array}{l} f(x+y)-k...

Channel:
Subscribers:
445,000
Published on ● Video Link: https://www.youtube.com/watch?v=9uhCsKJExTk



Duration: 6:24
0 views
0


A function \( f: \mathrm{R} \rightarrow \mathrm{R} \) is defined by
\[
\begin{array}{l}
f(x+y)-k x y=f(\mathrm{x})+2 y^{2} \forall x, y \in \mathrm{R} \\
\text { and } f(1)=2 ; f(2)=8
\end{array}
\]
where \( k \) is some constant, the \( f(x+y) \cdot f\left(\frac{1}{x+y}\right) \) equal to: (where \( x+y \neq 0 \) )
(a) 1
(b) 4
(c) \( k \)
(d) \( f(1) \)
📲PW App Link - https://bit.ly/YTAI_PWAP
🌐PW Website - https://www.pw.live




Other Videos By PW Solutions


2023-06-08\( \begin{array}{ll}\text { Comprehension } & : \text { If the function } f(x) \text { satisfies...
2023-06-08\( \begin{array}{ll}\text { Comprehension } & \text { Let the function } f \text { be defined in...
2023-06-08\( \begin{array}{ll}\text { Comprehension } & \text { Let the function } f \text { be defined in...
2023-06-08Let \( f \) be an injective function such that \( f(x) f(y)+2=f(x) \) \( +f(y)+f(x y) \forall x,...
2023-06-08Which of the following statement(s) is/are correct? (a) Equation \( \operatorname{sgn}(x)=\sin ^...
2023-06-08\( \begin{array}{ll}\text { Comprehension } & \text { Let the function } f \text { be defined in...
2023-06-08The maximum value of the function defined by \( f(x)=\min \) \( \left(e^{x}, 2+e^{2}-x, 8\right)...
2023-06-08If \( f: R \rightarrow \mathrm{R} \) is an invertible function such that \( f(x) \) and \( f^{-1...
2023-06-08Let \( f \) be a constant function with domain \( R \) and \( g \) be a certain function with do...
2023-06-08Let: \( f: A \rightarrow B \) and \( g: B \rightarrow C \) be two functions and \( g \circ f: A ...
2023-06-08A function \( f: \mathrm{R} \rightarrow \mathrm{R} \) is defined by \[ \begin{array}{l} f(x+y)-k...
2023-06-08Match the following
2023-06-08Let \( f, g: \mathrm{R} \rightarrow \mathrm{R} \) be defined by \( f(x)=3 x-1+|2 x+1| \) and \( ...
2023-06-08Solve graphically (i) \( \left|x^{2}-x\right|2 \) (ii) \( |x|-2 \geq|4-x| \)
2023-06-08\[ \begin{array}{l} \text { If } f ;(0, \infty) \rightarrow N \text { and } f(x)=\left[\frac{x^{...
2023-06-08Let \( \mathrm{f} \) be a real valued function such that for any real \( x \), \( f(15+x)=f(15-x...
2023-06-08Let \( f(x)=\left(\frac{1-x}{1+x}\right), 0 \leq x \leq 1 \) and \( g(x)=4 x(1-x), 0 \leq x \leq...
2023-06-08If \( R \) be a relation \( \) from \( A=\{1,2,3,4\} \) to \( B=\{1,3,5\} \) i.e., \( (a, b) \i...
2023-06-08The domain of the function \( f(x)=\sqrt{x^{12}-x^{9}+x^{4}-x+1} \) is (a) \( (-1,1) \) (b) \( (...
2023-06-08If \( f(x)+f(x+4)=f(x+2)+f(x+6) \forall x \in R \), and \( f(5)=10 \), then \( \sum_{r=1}^{100} ...
2023-06-08The range of \( f(x)=[\sin x+[\cos x+[\tan x+[\sec x]]]] \), \( x \in(0, \pi / 3) \), where [.] ...