Functions practice · Easy

The function $f(x)=\log \left(x+\sqrt{x^2+1}\right)$, is

In above problem, the range of $f(x) \forall x \in[-1,1]$ is

Function $\sin ^{-1} \sqrt{x}$ is defined in the interval

Function $f: N \rightarrow N, f(x)=2 x+3$ is:

The value of $b$ and $c$ for which the identit $f(x+1)-f(x)=8 x+3$ is satisfied, wher $f(x)=b x^{2}+c x+d$, are

If $f(x)=a x+b$ and $g(x)=c x+d$, then $f(g(x))=g(f(x))$ $\Leftrightarrow$

The range of the function $f(x)=\cos [x]$ for $-\pi / 2$ $< x < \pi / 2$ contains

If a function $f$ satisfies $f\left\{ {f\left( x \right)} \right\} = x + 1$ for all real values of $x$ and if $f\left( 0 \right) = \frac{1}{2}$, then $f\left( 1 \right)$ is equal to

If $f(x)=x^{b}+3, g(x)=a x+c$. If $(g(f(x)))^{-1}=\left(\frac{x-7}{2}\right)^{\frac{1}{3}}$, then $f o g(a c)+g o f(b)$ is:

Set $A$ has 3 elements and set $B$ has 4 elements. The number of injection that can be defined from $A$ to $B$ is

The domain of the function $f(x)=\sqrt{x-x^{2}}+\sqrt{4+x}+\sqrt{4-x}$ is

Given $f(x)=\frac{1}{(1-x)}, g(x)=f\{f(x)\}$ and $h(x)=f[f\{f(x)\}]$. Then the value of $f(x) \cdot g(x) . h(x)$ is

Let a function $f:N \to N$ be defied by $f\left( n \right) = \left[ {\begin{array}{cccccccccccccccccccc} {2n,}&{n = 2,4,6,8....} \\ {n - 1,}&{n = 3,7,11,15....} \\ {\frac{{n + 1}}{2},}&{n = 1,5,9,13....} \end{array}} \right.$ then $f$ is

If $f\left( x \right) = \left[ {x - 2} \right]$, where $\left[ x \right]$ denotes the greatest integer less than or equal to $x$, then $f\left( {2,\;5} \right)$ is equal to

The domain of definition of the function

$f\left( x \right) = {\log _3}\left\{ { - {{\log }_4}\left( {\frac{{6x - 4}}{{6x + 5}}} \right)} \right\},\;\mathrm{is}$

Let $f(x) = {a^x}(a > 0)$ be written as $f(x) = {f_1}(x) + {f_2}(x),$ where ${f_1}(x)$ is an even function and ${f_2}(x)$ is an odd function. Then ${f_1}(x + y) + {f_1}(x - y)$ equals

Let $g\left( x \right) = 1 + x - \left[ x \right]$ and $f\left( x \right) = \left\{ {\begin{array}{cccccccccccccccccccc} {\begin{array}{cccccccccccccccccccc} { - 1,\;\;\;\;\;\;\;\;\;\;x < 0\;\;\;\;\;\;}\\ {0,\;\;\;\;\;\;\;\;\;\;\;\;\;x = 0,\;} \end{array}}\\ {1\;\;\;\;\;\;\;\;\;\;\;\;x > 0\;\;\;} \end{array}} \right.\;\mathrm{then}\;\mathrm{\;for}$ for $x,f\left[ {g\left( x \right)} \right]$ is equal to

Domain of $f(x)=\log |\log x|$ is

If $f(x)=\frac{x}{x-1}=\frac{1}{y}$, then $f(y)=$

Let $\mathrm{A}$ and $\mathrm{B}$ be non-empty sets. Let $f: \mathrm{A} \rightarrow \mathrm{B}$ and $g: \mathrm{B} \rightarrow \mathrm{A}$ be two functions such that $f(g(x))=x, \forall x \in \mathbf{B}$. Which of the following statements are true (T) or false (F) ?
(i) The function $f$ is one-one function
(ii) The function $f$ is onto
(iii) The function $g$ is one-one
(iv) The function $g$ is onto

If $\mathrm{f}: \mathrm{R} \rightarrow \mathrm{R}, \mathrm{f}(\mathrm{x})=\left\{\begin{array}{ll}\mathrm{x}|\mathrm{x}|-4, & x \in Q \\ \mathrm{x}|\mathrm{x}|-\sqrt{3} & x \notin Q\end{array}\right.$, then $\mathrm{f}(\mathrm{x})$ is

Let $A = \{ 1,\,\,2,\,\,3,\,\,...,\,\,10\}$ and $f:A \to A$ be defined as $f(k) = \left\{ \begin{array}{l} k + 1,\quad if\,\,k\,\,is\,\,odd\\ k,\quad {\kern 1pt} {\kern 1pt} \quad if\,\,k\,\,is\,\,even \end{array} \right.$
Then, the number of possible functions $g:A \to A,$ such that $gof = f$ is

The domain of the function $f(x)=\sin ^{-1}\left[2 x^2-3\right]+\log _2\left(\log _{\frac{1}{2}}\left(x^2-5 x+5\right)\right),$ where $[t]$ is the greatest integer function, is

Let $f(x)=9^x /\left(9^x+3\right)$ for all $x \in \mathbb{R}$. Then the value of $\sum_{r=1}^{2008} f(r / 2009)$ is

If $f(x)=\frac{\log _e(x+3)}{x^2+3 x+2}$, then the domain of $f^{\prime}(x)$ is

Range of the function $f(x)=\sin ^{2}\left(x^{4}\right)+\cos ^{2}\left(x^{4}\right)$ is

If $f(x)=x^2+\lambda x+1$ for all real $x$ and $f$ is an even function, then the value of $\lambda$ is

If $f\left( x \right) = {\left( {25 - {x^4}} \right)^{1/4}}\;for\;0 < x < \sqrt 5 ,$ then $\left( {f\left( {\frac{1}{2}} \right)} \right) =$

The mapping $f:N \to N$ given $f\left( n \right) = 1 + {n^2},\;n \in N$ where $N$ is the set of natural number, is

The function $f\left( x \right) = \mathrm{sec}\left[ {\log (x + \sqrt {1 + {x^2})} } \right]$ is