`f(x) = x^2 +1 ,0 le x le 2 `
find the range of the function f.

Find the range of the function f(x)=x^2-2x-4.

Find the range of the function f(x)=(1)/(2+sin3x) .

Let f(x)=2x(2-x), 0 le x le 2 . Then find the number of solutions of f(f(f(x)))= (x)/(2) .

Consider the functions f(x)={(x+1",",x le 1),(2x+1",",1lt x le 2):} and g(x)={(x^(2)",", -1 le x lt2),(x+2",",2le x le 3):} The range of the function f(g(x)) is

A = { -2,-1,1,2} and f = { ( x , (1)/(x) ) : x in A } . Write down the range of f. Is f a function from A to A ?

Draw the graph of the function f(x)= x- |x-x^(2)|, -1 le x le 1 and find the points of non-differentiability.

A function f : (1,6) rarr R is defined as follows f(x) = {{: (1 + x, " " 1 le x lt 2 ),(2x - 1, " " 2 le x lt 4 ),(3 x^(2) -10, " " 4 le x lt 6 ):} (here , (1,6) = (x in R : 1 le x lt 6 ) ) Find the value of (i) f (5) (ii) f (3) (iii) f(1) (iv) f (2) - f(4) (v) 2 f(5) - 3 f(1).

A continuous random varibale X has probability density function f(x)=kx^(2) 0 le x lt 1 find k find distrubution function

Let f(x)=f_1(x)-2f_2 (x) , where ,where f_1(x)={((min{x^2,|x|},|x|le 1),(max{x^2,|x|},|x| le 1)) and f_2(x)={((min{x^2,|x|},|x| lt 1),({x^2,|x|},|x| le 1)) and let g(x)={ ((min{f(t):-3letlex,-3 le x le 0}),(max{f(t):0 le t le x,0 le x le 3})) for -3 le x le -1 the range of g(x) is