Consider the following in respect of the function f(x) = 10^x :

1. Its domain is (-∞, ∞)

2. It is a continuous function

3. It is differentiable at x = 0

Which of the above statements are correct?

In which one of the following intervals is the function $f(x) = \frac{x^3}{3}-\frac{7x^2}{2} + 6x + 5$ decreasing?

Consider the following statements:

1. A function f : Z → Z, defined by f(x) = x + 1, is one-one as well as onto.

2. A function f : N → N, defined by f(x) = x + 1, is one-one but not onto.

Which of the above statements is/are correct?

If 

$f(x)=\left|\begin{array}{ccc}1 & 1 & x+1 \\ 2 x & x(x-1) & x(x+1) \\ 3 x(x-1) & 2(x-1)(x-2) & x(x+1)(x-1)\end{array}\right|$ 

then what is f(-1) + f(0) + f(1) equal to?