Question

# If $$f(x)$$ is a polynomial in $$x(>0)$$ satisfying the equation $$f(x)+f\left (\dfrac1x\right)=f(x).f\left (\dfrac1x\right)$$ and $$f(2)=-7$$,  then $$f(3)$$ is equal to

A
26
B
27
C
28
D
29

Solution

## The correct option is A $$-26$$Whenever, $$f(x)+f\left (\dfrac{1}{x}\right)=f(x).f\left (\dfrac{1}{x}\right)$$, then $$f(x)=1+x^n$$ or $$f(x)=1-x^n$$ keeping in mind that $$n$$ must be greater than $$0$$.So here, $$f(2)=-7$$.So we choose $$f(x)=1-x^n$$.So, $$f(2)=1-2^n$$$$\Rightarrow 2^n=8$$$$\Rightarrow n=3$$So, the function is $$f(x)=1-x^3$$.Now,$$f(3)=1-3^3$$$$\Rightarrow f(3)=-26$$Mathematics

Suggest Corrections

0

Similar questions
View More

People also searched for
View More