​If f(x) = 4x + 1 and g(x) = kx + 2 such that fog(x) = gof(x), then what is the value of k ?

Consider the following statements in respect of the function f(x) = $\left\{\begin{array}{rc}|x|+1, & 0<|x| \leqslant 3 \\ 1, & x = 0\end{array}\right.$

1. The function attains maximum value only at x = 3

2. The function attains local minimum only at x = 0

Which of the statements given above is/are correct ?

Consider the following statements in respect of the function y = [x], x ∈ (-1, 1) where [.] is the greatest integer function:

1. Its derivative is 0 at x = 0.5

2. It is continuous at x = 0

Which of the above statements is/are correct?

What is the domain of the function $f(x) =\sqrt{1 - (x-1)^2} \ ?$