Home
Class 12
MATHS
Let f (x) = x^3-x^2-x+1 and g(x) = {max{...

Let `f (x) = x^3-x^2-x+1` and `g(x) = {max{f(t); 0<=t<=x}, 0<=x<=1, 3-x, 1<=x<=2` Discuss the continuity and differentiability of the function g (x) in the interval (0, 2).

Text Solution

AI Generated Solution

Promotional Banner

Similar Questions

Explore conceptually related problems

if f(x)=4x^3-x^2-2x+1 and g(x)={min f(t): 0<=t<=x; 0<=x<=1, 3-x : 1} then g(1/4)+g(3/4)+g(5/4) is equal to

Let f(x) = sin x and " g(x)" = {{:(max {f(t)","0 le x le pi},"for", 0 le x le pi),((1-cos x)/(2)",","for",x gt pi):} Then, g(x) is

Let f(x) = x^(2) + 2x +5 and g(x) = x^(3) - 1 be two real functions. Find (f+g)(x), (f-g)(x), (fg)(x) and ((f)/(g))(x) .

Let g(x) = x - [x] - 1 and f(x) = {{:(-1", " x lt 0),(0", "x =0),(1", " x gt 0):} [.] represents the greatest integer function then for all x, f(g(x)) = .

Let f(x) = 1 + 4x - x^(2), AA x in R g(x) = max {f(t), x le t le (x + 1), 0 le x lt 3min {(x + 3), 3 le x le 5} Verify conntinuity of g(x), for all x in [0, 5]

Let f(x) = max{|x^2 - 2 |x||,|x|} and g(x) = min{|x^2 - 2|x||, |x|} then

Let f(x) = 3x^(2) + 6x + 5 and g(x) = x + 1 be two real functions. Find (f+g)(x), (f-g)(x), (fg)(x) and ((f)/(g))(x)

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

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

Let f(x)=x^2+xg^2(1)+g^''(2) and g(x)=f(1).x^2+xf'(x)+f''(x), then find f(x) and g(x).