Show that f is continuous on (-infty , infty): f(x)={(x^2 if x<1)/(sqrt(x) if xge 1)}

abrigairaic

abrigairaic

Answered question

2022-08-05

Show that f is continuous on ( , ):
f ( x ) = { x 2   i f   x < 1 x   i f   x 1 }

Answer & Explanation

Dominic Paul

Dominic Paul

Beginner2022-08-06Added 17 answers

x 2 is continue function in ( , 1 )
x is continue in [ 1 , )
now we need to know if
lim x 1 f ( x ) = lim x 1 + f ( x ) = f ( 1 )...(1)
if it is, the function continue
f ( 1 ) = 1 = 1
lim x 1 f ( x ) = lim x 1 x 2 = 1
lim x 1 + f ( x ) = lim x 1 + x = 1
so (1) exists, the function is continue at x = 1
thus, the function is continue on ( , )

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