Functions · Mathematics · KCET

Domain of the function $f$, given by $f(x)=\frac{1}{\sqrt{(x-2)(x-5)}}$ is

If $f(x)=\sin \left[\pi^2\right] x-\sin \left[-\pi^2\right] x$, where $[x]=$ greatest integer $\leq x$, then which of the following is not true?

Let the functions " f " and " g " be $\mathrm{f}:\left[0, \frac{\pi}{2}\right] \rightarrow \mathrm{R}$ given by $\mathrm{f}(\mathrm{x})=\sin \mathrm{x}$ and $\mathrm{g}:\left[0, \frac{\pi}{2}\right] \rightarrow \mathrm{R}$ given by $g(x)=\cos x$, where $R$ is the set of real numbers

Consider the following statements:

Statement (I): $f$ and $g$ are one-one

Statement (II): $\mathrm{f}+\mathrm{g}$ is one-one

Which of the following is correct?

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

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

Let $(g \circ f)(x)=\sin x$ and $f \circ g(x)=(\sin \sqrt{x})^2$. Then,

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

If $$f(x)=a x+b$$, where $$a$$ and $$b$$ are integers, $$f(-1)=-5$$ and $$f(3)=3$$, then $$a$$ and $$b$$ are respectively

$$f: R \rightarrow R$$ and $$g:[0, \infty) \rightarrow R$$ defined by $$f(x)=x^2$$ and $$g(x)=\sqrt{x}$$. Which one of the following is not true?

Let $$f: R \rightarrow R$$ be defined by $$f(x)=3 x^2-5$$ and $$g: R \rightarrow R$$ by $$g(x)=\frac{x}{x^2+1}$$, then $$g \circ f$$ is

Let $$f(x)=\sin 2 x+\cos 2 x$$ and $$g(x)=x^2-1$$ then $$g(f(x))$$ is invertible in the domain

If the function is $$f(x)=\frac{1}{x+2}$$, then the point of discontinuity of the composite function $$y=f(f(x))$$ is

The domain of the function $$f(x)=\frac{1}{\log _{10}(1-x)}+\sqrt{x+2}$$ is

If $$f: R \rightarrow R$$ be defined by

$$f(x)=\left\{\begin{array}{llc} 2 x: & x>3 \\ x^2: & 1< x \leq 3 \\ 3 x: & x \leq 1 \end{array}\right.$$

then $$f(-1)+f(2)+f(4)$$ is

Domain of $$f(x)=\frac{x}{1-|x|}$$ is

$$f: R \rightarrow R$$ defined by $$f(x)$$ is equal to $$\left\{\begin{array}{l}2 x, x> 3 \\ x^2, 1< x \leq 3, \text { then } f(-2)+f(3)+f(4) \text { is } \\ 3 x, x \leq 1\end{array}\right.$$

Let $$A=\{x: x \in R, x$$ is not a positive integer) Define $$f: A \rightarrow R$$ as $$f(x)=\frac{2 x}{x-1}$$, then $$f$$ is

The function $$f(x)=\sqrt{3} \sin 2 x-\cos 2 x+4$$ is one-one in the interval

Domain of the function

$$f(x)=\frac{1}{\sqrt{\left[x^2\right]-[x]-6}},$$

where $$[x]$$ is greatest integer $$\leq x$$ is

Let $$f:[2, \infty) \rightarrow R$$ be the function defined $$f(x)=x^2-4 x+5$$, then the ranges of $$f$$ is

$$f: R \rightarrow R$$ and $$g:[0, \infty) \rightarrow R$$ is defined by $$f(x)=x^2$$ and $$g(x)=\sqrt{x}$$. Which one of the following is not true?

If $$|3 x-5| \leq 2$$ then

The value of $$\sqrt{24.99}$$ is

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

Let $f: R \rightarrow R$ be defined by
$f(x)=\left\{\begin{array}{lc}2 x ; & x > 3 \\ x^2 ; & 1 < x \leq 3 . \text { Then } \\ 3 x ; & x \leq 1\end{array}\right.$

$$ f(-1)+f(2)+f(4) \text { is }$$