Question

The function f(x) =(3x+5,if x<0)12x+5if x>0

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Answer 1

${\bold{\sf{LHS=lim_{x→0^{-}} (3x+5)}}}$

${\bold{\sf{LHS=3(0)+5=5}}}$

${\bold{\sf{RHS=lim_{x→0^{+}} (12x+5)}}}$

${\bold{\sf{RHS=12(0)+5=5}}}$

${\bold{\sf{f(0)=3x+5}}}$

${\bold{\sf{f(0)=3(0)+5=5}}}$

${\bold{lim_{x→0^{-}} f(x)=lim_{x→0^{+}} f(x) =f(0) =5}}$

${\bold{Therefore\:f(x)\:is\:a\:continuous\:function.}}$

${\bold{\sf{Because,}}}$

${\bold{\red{lim_{x→a^{-}} f(x)=lim_{x→a^{+}} f(x) =f(a) }}}$

${\bold{\red{Then \:f(x) \: is \: continuous \:function}}}$