Functions PYQs - Last 5 Years

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