Functions

The domain of the function $\sqrt{\dfrac{x-7}{9-x}}$ is

$f(x) = (x-1)^2$ for $x \geq 1$, $g(x)$ is a function whose graph is the reflection of the graph of $f(x)$ in the line $y = x$, then $g(x)$ is

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)=\c...

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?

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

Let $(g \circ f)(x)=\sin x$ and $f \circ g(x)=(\sin \sqrt{x})^2$. 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 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 $[x]^2-5[x]+6=0$, where $[x]$ denotes the greatest integer function, then

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

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

\(f: R \rightarrow R\) 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?

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

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

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

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

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

Domain of the function
\(f(x)=\frac{1}{\sqrt{\left[x^2\right]-[x]-6}},\)
where \([x]\) is greatest integer \(\leq x\) is

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

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

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

The value of \(\sqrt{24.99}\) is

If \(|3 x-5| \leq 2\) then

\(f: R \rightarrow R\) 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?

A is a set having 6 distinct elements. The number of distinct functions from $A$ to $A$ which are not bijections is

Let $f: R \rightarrow R$ be defined by $f(x)=\left\{\begin{array}{lc}2 x ; & x > 3 \\ x^2 ; & 1 < x \leq 3 . \text { Then } \\ 3 x ; & x \leq 1\end{array}\right.$
\(f(-1)+f(2)+f(4) \text { is }\)

Let $f, g: R \rightarrow R$ be two functions defined as $f(x)=|x|+x$ and $g(x)=|x|-x \forall x \in R$. Then $(f \circ g)(x)$ for $x<0$ is

Let $f(x)=x-\frac{1}{x}$, then $f(-1)$ is

If $|x+5| \geq 10$, then

The range of the function $f(x)=\sqrt{9-x^2}$ is

Binary operation * on $R-\{-1\}$ defined by $a^* b=\frac{a}{b+1}$ is

If $|x-2| \leq 1$, then

Let $f: R \rightarrow R$ be defined by $f(x)=x^4$, then

If $f(x)=8 x^3, g(x)=x^{1 / 3}$, then $f \circ g(x)$ is