If f(x) = $\frac{2\mathrm{x} - 1}{\mathrm{x} +\hspace{0.17em}5}; \left(\mathrm{x} \ne - 5\right)$, then f^-1(x) is equal to

• $\frac{\mathrm{x} + 5}{2\mathrm{x} - 1}, \mathrm{x} \ne \frac{1}{2}$

• $\frac{5\mathrm{x} + 1}{2 - \mathrm{x}}, \mathrm{x} \ne 2$

• $\frac{\mathrm{x} - 5}{2\mathrm{x} + 1}, \mathrm{x} \ne \frac{1}{2}$

• $\frac{5\mathrm{x} - 1}{\mathrm{x} - 2}, \mathrm{x} \ne 2$

A· {(B + C) x (A + B + C)} equals

• [A B C]

• [B A C]

• 0

• 1

Which is incorrect ?

• (AB)' = B'A'

• ${\left(\mathrm{AB}\right)}^{\mathrm{\theta }} = {\mathrm{B}}^{\mathrm{A}}{\mathrm{A}}^{\mathrm{\theta }}$

• $\overline{\mathrm{AB}} = \overline{\mathrm{B}} \overline{\mathrm{A}}$

• ${\left(\mathrm{AB}\right)}^{-1} = {\mathrm{B}}^{-1}{\mathrm{A}}^{-1}$

Cube root of 18 by using Newton-Raphson method will be

• 2.26

• 2.620

• 2.602

• None of these

The difference of the numbers (1100110011)₂ and (1101001011)₂ in binary system is

• (100000)₂

• (101010)₂

• (11000)₂

• (10111)₂

316.

If the function f · $\mathrm{f} . [1, \infty ) \to [1, \infty )$ is defined by f(x) = 2^{x(x - 1)}, then f^-1(x) is defined by

• ${\left(\frac{1}{2}\right)}^{\mathrm{x}\left(\mathrm{x} - 1\right)}$

• $\frac{1}{2}\left(1 \pm \sqrt{4{\log }_2\left(\mathrm{x}\right)}\right)$

• $\frac{1}{2}\left(1 - \sqrt{1 - 4{\log }_2\left(\mathrm{x}\right)}\right)$

• None of these

By Newton-Raphson method, the positive root of the equation x⁴ - x - 10 = 0 is

• 1.871

• 1.868

• 1.856

• None of these

Which of the following function is inverse of itself

• $\mathrm{f}\left(\mathrm{x}\right) = \frac{1 - \mathrm{x}}{1 + \mathrm{x}}$

• g(x) = 5^log(x)

• h(x) = 2^{x(x - 1)}

• None of the above

Let f : R $\to$ R be the function defined by f(x) = $\sqrt{\mathrm{x} - 3} \forall , \mathrm{x} \in \mathrm{R}$. Then f^-1(x) = ?

• x + 3

• x² + 3

• $\frac{\mathrm{x} + 3}{2}$

• $\frac{{\mathrm{x}}^2 + 3}{2}$

Let Z denote the set of integers define f : $\mathrm{Z} \to \mathrm{Z}$ by f(x) = $$\begin{gathered} \left\{\frac{\mathrm{x}}{2}, \mathrm{x} \mathrm{is} \mathrm{even} \\ 0, \mathrm{x} \mathrm{is} \mathrm{odd}\right\} \end{gathered}$$, then f is

• onto but not one-one

• one-one but not onto

• one-one and onto

• neither one-one nor onto