Functions · Mathematics · MHT CET

Range of the function $\mathrm{f}(x)=\frac{x^2+x+2}{x^2+x+1}, x \in \mathbb{R}$ is

If $[x]^2-5[x]+6=0$, where $[\cdot]$ denotes the greatest integer function, then

Let $\mathrm{f}(x)=(x+1)^2-1, x \geqslant-1$, then the set $\left\{x / f(x)=f^{-1}(x)\right\}$ is

If $\mathrm{f}:[1, \infty) \rightarrow[2, \infty)$ is given by $\mathrm{f}(x)=x+\frac{1}{x}$ then $\mathrm{f}^{-1}(x)$ equals

If $[x]^2-5[x]+6=0$, where $[x]$ denotes the greatest integer function, then

Let $\mathrm{f}(x)=\frac{a x}{x+1}, x \neq-1$, then for $\alpha=$ ________, $\mathrm{f}(\mathrm{f}(x))=x$.

The domain of definition of the function $y(x)$ is given by the equation $2^x+2^y=2$, is

The domain of definition of the function $f(x)$ given by the equation $2^x+2^y=2$ is

If $\mathrm{f}(x)=\frac{x}{2-x}, \mathrm{~g}(x)=\frac{x+1}{x+2}$, then (gogof) $(x)=$

The domain of definition of $\mathrm{f}(x)=\frac{\log _2(x+3)}{x^2+3 x+2}$ is

If $g(x)=x^2+x-1$ and (gof) $(x)=4 x^2-10 x+5$, then $\mathrm{f}(2)$ is equal to

For a suitable chosen real constant a, let a function $f: \mathbb{R}-\{-\mathrm{a}\} \rightarrow \mathbb{R}$ be defined by $f(x)=\frac{a-x}{a+x}$. Further suppose that for any real number $x \neq-\mathrm{a}$ and $\mathrm{f}(x) \neq-\mathrm{a}$, (fof) $(x)=x$. Then $f\left(-\frac{1}{5}\right)$ is equal to

If $$\mathrm{f}(x)=\frac{2 x-3}{3 x-4}, x \neq \frac{4}{3}$$, then the value of $$\mathrm{f}^{-1}(x)$$ is

The range of the function $$\mathrm{f}(x)=\frac{x^2}{x^2+1}$$ is

The function $$\mathrm{f}(x)=[x] \cdot \cos \left(\frac{2 x-1}{2}\right) \pi$$, where $$[\cdot]$$ denotes the greatest integer function, is discontinuous at

The domain of the definition of the function $$y(x)$$ is given by the equation $$2^x+2^y=2$$ is

If $$3 \mathrm{f}(x)-\mathrm{f}\left(\frac{1}{x}\right)=8 \log _2 x^3, x>0$$, then $$\mathrm{f}(2), \mathrm{f}(4)$$, $$f(8)$$ are in

If $$\mathrm{f}(x)=x^2+1$$ and $$\mathrm{g}(x)=\frac{1}{x}$$, then the value of $$\mathrm{f}(\mathrm{g}(\mathrm{g}(\mathrm{f}(x))))$$ at $$x=1$$ is

If $$\mathrm{g}(x)=1+\sqrt{x}$$ and $$\mathrm{f}(\mathrm{g}(x))=3+2 \sqrt{x}+x$$ then $$\mathrm{f}(\mathrm{f}(x))$$ is

The approximate value of $$\sin \left(60^{\circ} 0^{\prime} 10^{\prime \prime}\right)$$ is (given that $$\sqrt{3}=1.732,1^{\circ}=0.0175^{\circ}$$ )

If $$\mathrm{f}(x)=\frac{3 x+4}{5 x-7}$$ and $$\mathrm{g}(x)=\frac{7 x+4}{5 x-3}$$, then $$\mathrm{f}(\mathrm{g}(x))=$$

The domain of the function given by $$2^x+2^y=2$$ is

Let $$\mathrm{f}(x)=\mathrm{e}^x-x$$ and $$\mathrm{g}(x)=x^2-x, \forall x \in \mathrm{R}$$, then the set of all $$x \in \mathrm{R}$$, where the function $$\mathrm{h}(x)=(\mathrm{fog})(x)$$ is increasing is

$$\mathrm{f}: \mathrm{R} \rightarrow \mathrm{R} ; \mathrm{g}: \mathrm{R} \rightarrow \mathrm{R}$$ are two functions such that $$\mathrm{f}(x)=2 x-3, \mathrm{~g}(x)=x^3+5$$, then $$(\mathrm{fog})^{-1}(-9)$$ is

$$\mathrm{f}: \mathbb{R}-\left(-\frac{3}{5}\right) \rightarrow \mathbb{R}$$ is defined by $$f(x)=\frac{3 x-2}{5 x+3}$$, then $$f \circ f(1)$$ is

The number of discontinuities of the greatest integer function $$\mathrm{f}(x)=[x], x \in\left(-\frac{7}{2}, 100\right)$$

If $$[x]$$ is greatest integer function and $$2[2 x-5]-1=7$$, then $$x$$ lies in

If $$f(x)=2\{x\}+5 x$$, where $$\{x\}$$ is fractional part function, then $$f(-1.4)$$ is

If $$f(x)=\frac{x}{2 x+1}$$ and $$g(x)=\frac{x}{x+1}$$, then $$(f \circ g)(x)=$$

The domain of the function $$\log _{10}\left(x^2-5 x+6\right)$$ is

Range of the function $$f(x)=3+2^x+4^x$$ is

If $$f(x)=[8 x]-3$$, where $$[x]$$ is greatest integer function of $$x$$, then $$f(\pi)=$$ (where $$\pi=3,14$$)

The domain of the function $$f(x)=\sqrt{x-1}+\sqrt{6-x}$$ is

If f(x) = 3[x] + 5{x + 1}, where [x] is greatest integer function of x and {x} is fractional part function of x, then f($$-$$1.32) =

Let $$A=[a, b, c, d], B=[1,2,3]$$. Relation $$R_1, R_2, R_3, R_4$$ are as follows :

$$\begin{aligned} & R_1=[(\mathrm{a}, 1),(\mathrm{b}, 2),(\mathrm{c}, 1),(\mathrm{d}, 2)] \\ & \mathrm{R}_2=[(\mathrm{a}, 1),(\mathrm{b}, 1),(\mathrm{c}, 1),(\mathrm{d}, 1)] \\ & \mathrm{R}_3=[(\mathrm{a}, 2),(\mathrm{b}, 3),(\mathrm{c}, 2),(\mathrm{d}, 2)] \\ & \mathrm{R}_4=[(\mathrm{a}, 1),(\mathrm{b}, 2),(\mathrm{a}, 2),(\mathrm{d}, 3)] \text {, then } \end{aligned}$$

The domain of the function $$f(x)=\frac{1}{\sqrt{x+|x|}}$$ is

The range of the function $f(x)=\frac{x-3}{5-x}, x \neq 5$ is

For $$f(x)=[x]$$, where $$[x]$$ is the greatest integer function, which of the following is true, for every $$x \in \mathbf{R}$$

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

The approximate value of the function $$f(x)=x^3-3 x+5$$ at $$x=1.99$$ is

If $$f(x)=\frac{2 x+3}{3 x-2}, x \neq \frac{2}{3}$$, then the function $$f$$ of is

The domain of the real valued function $f(x)=\sqrt{\frac{x-2}{3-x}}$ is......

Which of the following function has period 2?

If $f(x)=3 x+6, g(x)=4 x+k$ and $f \circ g(x)=g \circ f(x)$ then $k=$

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