Functions - Calculus - Mathematics Previous Year Questions

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

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

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

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

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

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

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

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