Functions practice · Easy

The domain of the function $\sqrt{\log \left(x^{2}-6 x+6\right)}$ is

If the function $f:[1, \infty) \rightarrow[1, \infty)$ is defined by $f(x)=2^{x(x-1)}$ then $f^{-1}(x)$ is

If $f\left( x \right) = \frac{{1 - x}}{{1 + x}}\left( {x \ne - 1} \right)$, then ${f^{ - 1}}\left( x \right)$ equals to

The period of $f(x)=2 \cos \left(\frac{x-\pi}{3}\right)$ is

Suppose that $f$ is a periodic function with period $\frac{1}{2}$ and that $f(2)=5$ and $f\left(\frac{9}{4}\right)=2$ then $f(-3)-f\left(\frac{1}{4}\right)$ has the value equal to

The domain of definition of the function

$f\left( x \right) = {\log _2}\left[ { - {{\left( {{{\log }_2}x} \right)}^2} + 5{{\log }_2}x - 6} \right],$ is

The largest possible set of real numbers which can be the domain of $f\left( x \right) = \sqrt {1 - \frac{1}{x}}$ is

Let $f: R^{+} \rightarrow R$ be a function which satisfy $f(x) f(y)=f(x y)+2\left(\frac{1}{x}+\frac{1}{y}+1\right) \forall x, y>0$ then the value of $f\left(\frac{1}{2}\right)$ is

If $f(x)=x^2-1$ and $g(x)=3 x+1$, then $(g \circ f)(x)=$

Let $f(x)$ satisfies $\frac{f^2(x)}{f(1-x)}=x^3$, where $f(1-x) \neq 0$, then $f\left(\frac{1}{2}\right)$ equals

Let $f(x)=\left\{\begin{array}{r}1+|x| ; x<-1 \\ {[x] ; x \geqslant-1}\end{array}\right.$, where [.] denotes the greatest integer function. Then $\mathrm{f}\{\mathrm{f}(-2.3)\}$ equals -

The domain of the function $f(x)=\frac{1}{\sqrt{[x]^2-[x]-6}}$ is (where [.] denotes G.I.F)

The domain of definition of
$f\left( x \right) = {\log _{10}}\left\{ {1 - {{\log }_{10}}\left( {{x^5} - 5x + 16} \right)} \right\},$ is

The range of the function $f\left( x \right) = {x^2} - 6x + 7$ is

Given that $x, y$ and $b$ are real numbers and $x < y, b < 0$, then

The domain of ${\sin ^{ - 1}}\left[ {{{\log }_3}\left( {\frac{x}{3}} \right)} \right]$ is

If $\mathrm{f}: \mathrm{R} \rightarrow \mathrm{R}$ is defined by $f(x)=3 x+|x|$, then $f(2 x)-f(-x)-6 x=$

Let $\mathrm{A}=\left\{x_{1}, x_{2}, \ldots \ldots \ldots, x_{7}\right\}$ and $\mathrm{B}=\left\{y_{1}, y_{2}, y_{3}\right\}$ be two sets containing seven and three distinct elements respectively. Then the total number of functions $\mathrm{f}: \mathrm{A} \rightarrow \mathrm{B}$ that are onto, if there exist exactly three elements $x$ in A such that $\mathrm{f}(x)=y_{2}$, is equal to :

The domain of ${\sin ^{ - 1}}\left[ {{{\log }_2}\left( {\frac{x}{{12}}} \right)} \right]$ is

The domain of the function

$f\left( x \right) = {\log _{10}}\left( {\sqrt {x - 4} + \sqrt {6 - x} } \right)$ is

The domain of the function $f\left( x \right) = {\log _{3 + x}}\left( {{x^2} - 1} \right)$ is

The domain of definition of

$f\left( x \right) = {\log _{10}}\left\{ {{{\log }_{10}}\left( {1 + {x^3}} \right)} \right\},\;\mathrm{is}$

Let $f:R \to R,g:R \to R$ be two functions given by $f\left( x \right) = 2x - 3,g\left( x \right) = {x^3} + 5.$ Then, ${\left( {fog} \right)^{ - 1}}x$ is equal to

The solution set of the inequality $\mathrm{lo}{\mathrm{g}_{\mathrm{sin}\left( {\frac{\pi }{3}} \right)}}\left( {{x^2} - 3x + 2} \right) \ge 2$ is

Let $f: \mathrm{A} \rightarrow \mathrm{B}$ be a function defined as $f(x)=\frac{x-1}{x-2}$, where $A=R-\{2\}$ and $B=R-\{1\}$. Then $f$ is

The domain of the real function $f\left( x \right) = \frac{1}{{\sqrt {4 - {x^2}} }}$ is

The domain of the function $f\left( x \right) = {\log _{3 + x}}\left( {{x^2} - 1} \right)$ is

Let $f: R \rightarrow R$ be a function defined by $f(x)=x^3+4$, then $f$ is

Suppose that $f$ is continuous on $[\mathrm{a}, \mathrm{b}]$ and that $f(\mathrm{x})$ is an integer for each $\mathrm{x}$ in $[\mathrm{a}, \mathrm{b}]$. Then in $[\mathrm{a}, \mathrm{b}]$

Let $A = \left\{ {1,2,3} \right\}\;and\;B = \left\{ {2,3,4} \right\}$ then which of the following relations is a function from $A\;to\;B?$