We have, $f'(x) = \mathop {\lim }\limits_{h \to 0} \frac{{f(x + h) – f(x)}}{h}$

$ = \mathop {\lim }\limits_{h \to 0} \frac{{2xh + f(h)}}{h}$

$ = 2x + \mathop {\lim }\limits_{h \to 0} \frac{{f(h)}}{h}$ Continue reading f is differentiable function such that

$f(x + y) – f(x) = f(y) + 2xy$

$x,y \in R$

$f(x) = ?$ →

$x \to \frac{1}{x}$ in the original equation yields,

$f\left( {\frac{1}{x}} \right) + f(x) + 3f\left( { – \frac{1}{x}} \right) = \frac{1}{x}$ ……..(A)

Original equation – (A) yields,

$3f( – x) – 3f\left( { – \frac{1}{x}} \right) = x – \frac{1}{x}$ Continue reading Find $f(x)$ such that,

$f(x) + f\left( {\frac{1}{x}} \right) + 3f( – x) = x$ →

Let $f:R \to R$ be defined by $f(x) = \frac{{{x^2} – 3x – 6}}{{{x^2} + 2x + 4}}$. Then which of the following statements is(are) correct?

(A) f is onto
(B) Range of f is $\left[ { – \frac{3}{2},2} \right]$
(C) f is into
(D) Domain of f is [-4, 0] Continue reading $f(x) = \frac{{{x^2} – 3x – 6}}{{{x^2} + 2x + 4}}$

Domain/Range/Onto/Into →