Given that $f\left( x \right)$ is a differentiable function of $x$ and that $f\left( x \right).{\rm{ }}f\left( y \right) = f\left( x \right) + f\left( y \right) + f\left( {xy} \right) - 2$ and that $f\left( 2 \right) = 5$. Then, $f\left( 3 \right)$ is equal to

JEE MATHEMATICS MCQ: FUNCTIONS

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Application +4 | -1

Given that

f\left( x \right)

is a differentiable function of

x

and that

f\left( x \right).\mathrm{ }f\left( y \right) = f\left( x \right) + f\left( y \right) + f\left( {xy} \right) - 2

and that

f\left( 2 \right) = 5

. Then,

f\left( 3 \right)

is equal to

View answer and explanation

Correct option: A

Option A (10) is correct because by substituting y = 1/x into the given functional equation, we can determine that f(x) = x² + 1, and therefore f(3) = 10.

JEE MATHEMATICS MCQ: FUNCTIONS

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