Question

For \[f(x)=\begin{cases}x^3+3,&x\ne0\\1,&x=0\end{cases}\], which statement is correct at \[x=0\]?

Options

• \[f(0)=3\] and \[\lim_{x\to0}f(x)=3\], so \[f\] is continuous.

• \[f(0)=1\] and \[\lim_{x\to0}f(x)=3\], so \[f\] is discontinuous.

• \[f(0)\] is not defined and \[\lim_{x\to0}f(x)=3\].

• \[f(0)=1\] and \[\lim_{x\to0}f(x)=1\], so \[f\] is continuous.

Answer 1

The function value is specified as \[f(0)=1\]. For \[x\ne0\], the expression approaches \[0^3+3=3\], which is not equal to \[f(0)\].