Question

If \[f\] and \[g\] are continuous at \[x=c\], which collection is continuous at \[x=c\]?

Options

• \[\frac{f}{g}\] only when \[g(c)=0\]

• \[f+g,\ f-g,\text{ and }f\cdot g\]

• \[\tan x\] for every real \[x\]

• \[\frac{1}{g}\] whenever \[g(x)=0\]

Answer 1

If \[f\] and \[g\] are continuous at \[c\], then \[f+g\], \[f-g\], and \[fg\] are continuous at \[c\]. Addition, subtraction, and multiplication preserve continuity at the same real number.