Discuss the continuity of the function f given by `f(x)={x , ifxgeq0x^2, ifx<0`

Explanation

`f(x)={x` if `x≥0` `x^2` if `x<0}`

to check for continuity we find the left hand limit and right hand limit. If for a point 'a' in the domain `f(x)`


⇒LHL=RHL=`f(a)`


Then the function is continuous at `x=a`


for `x>0`



`f(x)=x,`


and we know that

`f(x)=x` ( identity function ) is a rational function well defined in the interval (0,∞) and is continuous,


For` x<0`


...