Let \( f \) be an injective function such that \( f(x) f(y)+2=f(x) \) \( +f(y)+f(x y) \forall x,...

Channel:
Subscribers:
443,000
Published on ● Video Link: https://www.youtube.com/watch?v=is9GppG0KQw



Duration: 8:14
0 views
0


Let \( f \) be an injective function such that \( f(x) f(y)+2=f(x) \) \( +f(y)+f(x y) \forall x, y \in R \). If \( f(4)=65 \) and \( f(0) \neq 2 \), then \( f(\mathrm{x}) \) is equal to, \( \forall x \in R \).
(a) \( x^{3}-1 \)
(b) \( x^{3}+2 \)
(c) \( x^{3}+1 \)
(d) \( x^{2}+49 \)
📲PW App Link - https://bit.ly/YTAI_PWAP
🌐PW Website - https://www.pw.live




Other Videos By PW Solutions


2023-06-08The maximum value of the function defined by \( f(x)=\min \) \( \left(e^{x}, 2+e^{2}-x, 8\right)...
2023-06-08\( \begin{array}{ll}\text { Comprehension } & \text { : If the function } f(x) \text { satisfies...
2023-06-08Let: \( f: A \rightarrow B \) and \( g: B \rightarrow C \) be two functions and \( g \circ f: A ...
2023-06-08\( \begin{array}{ll}\text { Comprehension } & : \theta \text { is said to be well behaved if it ...
2023-06-08\( \begin{array}{ll}\text { Comprehension } & : \text { If the function } f(x) \text { satisfies...
2023-06-08Comprehension \( \quad: \) Consider a function \( f: R \rightarrow R \) such that \( (f(x)+f(z))...
2023-06-08Show that \( \left(f \circ f^{-1}\right)(x)=\left(f^{-1} \mathrm{\circ} f\right)(x)=x \) for (i)...
2023-06-08Comprehension \( \quad: \) Consider a function \( f: R \rightarrow R \) such that \( (f(x)+f(z))...
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...
2023-06-08Let \( f \) be an injective function such that \( f(x) f(y)+2=f(x) \) \( +f(y)+f(x y) \forall x,...
2023-06-08\( \begin{array}{ll}\text { Comprehension } & \text { Let the function } f \text { be defined in...
2023-06-08If \( f: R \rightarrow \mathrm{R} \) is an invertible function such that \( f(x) \) and \( f^{-1...
2023-06-08\( \begin{array}{ll}\text { Comprehension } & \text { Let the function } f \text { be defined in...
2023-06-08Solve graphically (i) \( \left|x^{2}-x\right|2 \) (ii) \( |x|-2 \geq|4-x| \)
2023-06-08A function \( f: \mathrm{R} \rightarrow \mathrm{R} \) is defined by \[ \begin{array}{l} f(x+y)-k...
2023-06-08Let \( f \) be a constant function with domain \( R \) and \( g \) be a certain function with do...
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 \( ...
2023-06-08Let \( f(x)=\left(\frac{1-x}{1+x}\right), 0 \leq x \leq 1 \) and \( g(x)=4 x(1-x), 0 \leq x \leq...
2023-06-08\[ \begin{array}{l} \text { If } f ;(0, \infty) \rightarrow N \text { and } f(x)=\left[\frac{x^{...