List of top Mathematics Questions on Functions asked in KCET

Let $f : \mathbb{R} \to \mathbb{R}$ be defined by $f(x) = x^2 + 1$. Then the pre-images of $17$ and $-3$ respectively are:

Let the function satisfy the equation $f(x + y) = f(x)f(y)$ for all $x, y \in \mathbb{R}$, where $f(0) \neq 0$. If $f(5) = 3$ and $f'(0) = 2$, then $f'(5)$ is:

f : R → R and g : [0, ∞) → R are defined by f(x) = x² and g(x)=\(\sqrt{x}\). Which one of the following is not true ?

At x = 1, the function f(x) = \(\left\{ \begin{aligned}     & x^3-1\ \ \ \ \ \ 1<x<\infin \\     & x-1\ \ \ \ \ -\infin<x≤1 \\      \end{aligned} \right.\) is

The function f(x) = \(\sqrt3\) sin2x - cos2x + 4 is one-one in the interval

f : R → R defined by f(x) = \(\left\{ \begin{aligned}     & 2x;x>3 \\     &x^2;1<x≤3\\     & 3x;x≤1 \end{aligned} \right.\) then f(-2) + f(3) + f(4) is

The cost and revenue functions of a product are given by c(x) = 20x + 4000 and R(x) = 60x + 2000 respectively where x is the number of items produced and sold. The value of x to earn profit is

Domain of f(x) = \(\frac{x}{|-|x|}\) is

Let f : [2, ∞) → R be the function defined by f(x) = x² - 4x + 5 , then the range of f is

If f(x) = $\sin^{-1}$ $\left(\frac{2x}{1+x^{2}}\right)$, then f' $(\sqrt{3})$ is

The domain of the function f : R $\to$ R defined by $f(x) = \sqrt{x^2 - 7x + 12} $ is

If $ f(x) = 2-2x^2,$ find $\frac {f(3,8)-f(4)} {3.8-4} $,

The domain of the function $f(x) = \sqrt {\cos x}$ is

The domain of $ f(x) = sin^{-1} [Log_2 (\frac {x} {2})] $ is

If y=2x^3x,then \(\frac{dy}{dx}\) at x=1 is

The function f(x) = |cos x| is

Let the function satisfy the equation f (x + y) = f(x)f(y) for all x, y ∈ R, where f (0)≠0. If f (5) = 3 and f'(0)=2, then f'(5) is