If `phi (x)=f(x)+f(2a-x)` and `f'(x) gt a, a gt 0, 0 le x le 2a`, then

Let f(x) be defined on [-2,2] and is given by f(x) = {{:(x+1, - 2le x le 0 ),(x - 1, 0 le x le 2):} , then f (|x|) is defined as

If f((1)/(x)) +x^(2)f(x) =0, x gt0 and I= int_(1//x)^(x) f(t)dt, (1)/(2) le x le 2x , then I is equal to

If f((1)/(x)) +x^(2)f(x) =0, x gt0 and I= int_(1//x)^(x) f(t)dt, (1)/(2) le x le 2x , then I is equal to

The probability density function of X is given by f(x)={{:(kxe^(-2x), "for " x gt 0), (0, "for " x le 0):} Find the value of k.

f(x){{:(2x "," if x lt 0 ),(0"," if 0 le x le 1),(4x "," if x gt 1 ):}

If f(x)=2x-1, " if " x gt1, =x^(2)+1," if " -1 le xle1," then "(f(1)+f(3)+f(0))/(f(2)+f(-1)+f(1//2))=

If the probability density function of a random variable X is f(x)=x/2 in 0 le x le 2 , then P(X gt 1.5 | X gt 1) is equal to