Determine if the following functions are continuous on the c

Determine if the following functions are continuous on the closed interval. f(x) = x^2 - 4x - 5 [-1, 5] f(x) = x, x lessthanorequalto 0 x + 1, x > 0 [-3, 3]

Solution

36)     f(x) = x^2 - 4x - 5 [ -1, 5 ]

f(x) is a quadratic function which is continous over the interval [ -1, 5]

Interval over which it is continous : ( - inf , inf)

37)   f(x) = x , x<=0

               = x+1 , x >0   [ -3, 3]

At x =0 ;f(x) = x f(0) = 0

At x = 0 ;f(x) = x+1 ; f(0) = 1

The two values of f(0) are not same

So, there f(x) is discontinous at x =0

So, f(x) is continous in the interval : ( -inf , 0) U (0, inf)