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  • If  <img alt="f(x)\cdot f(y)=f(x)+f(y)+f(xy)-2\; \; \forall \; x,\; y\: \in \: R" src="https://learn.careers360.com/latex-image/?f%28x%29%5Ccdot%20f%28y%29%3Df%28x%29&plus;f%28y%29&plu

If  f(x)\cdot f(y)=f(x)+f(y)+f(xy)-2\; \; \forall \; x,\; y\: \in \: R and if f(x)is not a constant function, then the value of f(1) is equal to

Option: 1 1

Option: 2 2

Option: 3 0

Option: 4 3

Answers (1)

best_answer

As we have learnt in

 

Constant Function -

f\left ( x \right )= c,\: \: \: \forall x\in A

if f:A\rightarrow B\: and \: c is a constant value.

- wherein

 

 

Put x=y=1,(f(1))^{2}=3f(1)-2

\Rightarrow f(1)=1\: or\: 2

Let\: f(1)=1, then\: put\: y=1

f(x).f(1)=f(x)+f(1)+f(x)-2

f(x)=1

constant function but f(x)  is not constant function

\therefore f(1)\neq 1, hence f(1)=2

 

Posted by

Rishabh

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