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Maths-

General

Easy

Question

If f(x) is a differentiable real valued function satisfying $f to the power of ´ ´ end exponent left parenthesis x right parenthesis minus 3 f to the power of ´ end exponent left parenthesis x right parenthesis greater than 3 for all x greater or equal than 0$ and $f to the power of ´ left parenthesis 0 right parenthesis equals negative 1 comma$ then $f left parenthesis x right parenthesis plus x for all x greater than 0$ is

decreasing function of x
increasing function of x
constant function
none of these

The correct answer is: increasing function of x

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Statement 2 : $f open parentheses x subscript 1 end subscript close parentheses greater than f open parentheses x subscript 2 end subscript close parentheses for all x subscript 1 end subscript element of open parentheses 2 comma 4 close parentheses text and end text x subscript 2 end subscript element of open parentheses 0 comma 2 close parentheses union open parentheses 4 comma infinity close parentheses$

Let $f left parenthesis x right parenthesis equals fraction numerator ln invisible function application x over denominator x end fraction for all x greater than 0 comma$ then
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If f(x) is a polynomial function such that $f open parentheses x close parentheses f open parentheses fraction numerator 1 over denominator x end fraction close parentheses equals f open parentheses x close parentheses plus f open parentheses fraction numerator 1 over denominator x end fraction close parentheses$ for all non zero real values of x and f(4) = -15 then f(3) + f(-3) =

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