Question

Let $f:R→R$ be a function defined by f(x)={$3e^x \text{ if } x<0 x^2+3x+3 \text{ if } 0≤x<1 x^2-3x-3\text{ if } x≥1$

• A. f is continuous on R
• B. f is not continuous on R
• C. f is continuous on R\{0}
• D. f is continuous on R\{1}
• E. f is not continuous on R\{0,1}

Answer 1

Answer: (C)

f is continuous on R\{0}

Answer 2

As per the given data we can proceed as follows

$f(0^-)=3$

$f(0^+)=3=f(0)$

\therefore $f$ is continuous at x=0.

$f(1^-)=7$

$f(1^+)=-5$

So,$f$is discontinuous at x$= 1$

$∴$ ,$f$ is continuous on $R$ \ {${1}$}