Let `f(x)=1+x`, `0 leq x leq 2` and `f(x)=3−x`,`2 lt x leq 3`. Find `f(f(x))`.

Let f(x)={{:(1+x",", 0 le x le 2),(3-x"," ,2 lt x le 3):} find (fof) (x).

Let f_1(x)={x, x leq x leq 1 and 1 x gt1 and 0 ,otherwise f_2(x) =f_1 (-x) for all x abd f_3(x)=-f_2(x) for all x and f_4(x)=-f_3(-x) for all x Which of the following is necessarily true?

Let f(x)={(2x+a",",x ge -1),(bx^(2)+3",",x lt -1):} and g(x)={(x+4",",0 le x le 4),(-3x-2",",-2 lt x lt 0):} If the domain of g(f(x))" is " [-1, 4], then

Let f(x)={x+1,x >0, 2-x ,xlt=0 and g(x)={x+3,x 0)g(f(x)).

Let f : R rarr given by f(x) = 3x^(2) + 5x + 1 . Find f(0), f(1), f(2).

Let f(x) ={:{(x, "for", 0 le x lt1),( 3-x,"for", 1 le x le2):} Then f(x) is

Let f:[0,1]rarrR (the set of all real numbers) be a function. Suppose the function f is twice differentiable, f(0)=f(1)=0 and satisfies f\'\'(x)-2f\'(x)+f(x) ge e^x, x in [0,1] If the function e^(-x)f(x) assumes its minimum in the interval [0,1] at x=1/4 , which of the following is true? (A) f\'(x) lt f(x), 1/4 lt x lt 3/4 (B) f\'(x) gt f(x), 0 lt x lt 1/4 (C) f\'(x) lt f(x), 0 lt x lt 1/4 (D) f\'(x) lt f(x), 3/4 lt x lt 1

Let f:[0,1]rarrR (the set of all real numbers) be a function. Suppose the function f is twice differentiable, f(0)=f(1)=0 and satisfies f'(x)-2f\'(x)+f(x) ge e^x, x in [0,1] If the function e^(-x)f(x) assumes its minimum in the interval [0,1] at x=1/4 , which of the following is true? (A) f\'(x) lt f(x), 1/4 lt x lt 3/4 (B) f\'(x) gt f(x), 0 lt x lt 1/4 (C) f\'(x) lt f(x), 0 lt x lt 1/4 (D) f\'(x) lt f(x), 3/4 lt x lt 1

Let f(x) be defined on [-2,2] and be given by f(x)={(-1",",-2 le x le 0),(x-1",",0 lt x le 2):} and g(x)=f(|x|) +|f(x)| . Then find g(x) .

Let f (x)= {{:(2-x"," , -3 le x le 0),( x-2"," , 0 lt x lt 4):} Then f ^(-1) (x) is discontinous at x=