Show that

f

is continuous on

(-\\\\infty ,\\\\infty )

.\

f(x)={(1-x^(2) if x1):}

\ On the interval

(-\\\\infty ,1),f

is ] function; therefore

f

is continuous on

(-\\\\infty ,1)

.\ On the interval

(1,\\\\infty ),f

is function; therefore

f

is continuous on

(1,\\\\infty )

.\ At

x=1

,\

\\\\lim_(x->1^(-))f(x)=\\\\lim_(x->1^(-))(,)=

\ and\

\\\\lim_(x->1^(+))f(x)=\\\\lim_(x->1^(+))()=

\ so

\\\\lim_(x->1)f(x)=

\ Also,

f(1)=