If * is the operation defined by a b = ab for a, b $\in$ N, then (2 * 3) * 2 is equal to

• 81

• 512

• 216

• 64

The domain of the function f(x) $$\begin{gathered} \left\{\left({\mathrm{x}}^2 - 9\right)/\left(\mathrm{x} - 3\right), \mathrm{if} \mathrm{x} \ne 3 \\ 6, \mathrm{if} \mathrm{x} = 3\right\} \end{gathered}$$ is

• (0, 3)

• $\left(- \infty , 3\right)$

• $\left(- \infty , \infty \right)$

• $\left(3, \infty \right)$

Let f(x) = x³ and g(x) = 3^*. The values of A such that g[f (A)] = f[g(A)] are

• 0, 2

• 1, 3

• 0, $\pm$ 3

• 0, $\pm \sqrt{3}$

If $\mathrm{f}\left(\frac{\mathrm{x} + 1}{2\mathrm{x} - 1}\right) = 2\mathrm{x}, \mathrm{x} \in \mathrm{N}$, then the value of f(2) is equal to

• 1

• 4

• 3

• 2

For all rest numbers x and y, it is known as the real valued function f satisfies f(x) + f(y) = f(x + y). If f(1) = 7, then $\sum _{\mathrm{r} = 1}^{100}\mathrm{f}\left(\mathrm{r}\right)$ is equal to

• 7 x 51 x 102

• 6 x 50 x 102

• 7 x 50 x 102

• 7 x 50 x 101

If f(x) = $\frac{\mathrm{x} + 1}{\mathrm{x} - 1}$, then the value of f(f(x)) is equal to

• x

• 0

• - x

• 1

If $\mathrm{f}\left(\mathrm{x}\right) = \frac{1 - \mathrm{x}}{1 + \mathrm{x}}\left(\mathrm{x} \ne - 1\right)$, then f^-1(x) equals to :

• f(x)

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

• - f(x)

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

518.

Let S be the set of all real numbers. Then the relation R = {(a, b): 1 + ab > 0} on S is :

• reflexive and symmetric but not transitive

• reflexive and transitive but not symmetric

• symmetric and transitive but not reflexive

• reflexive, transitive and symmetric

Let $\mathrm{f}\left(\mathrm{x} + \frac{1}{\mathrm{x}}\right) = {\mathrm{x}}^2 + \frac{1}{{\mathrm{x}}^2}, \mathrm{x} \ne 0$, then f(x) equals to :

• x²

• x² - 1

• x² - 2

• x² + 1

Let f : R $\to$ R : f(x) = x² and g : R $\to$ R : g(x) = x + 5, then gof is :

• (x + 5)

• (x + 5²)

• (x² + 5²)

• (x² + 5)