Exercise · ZW-CONTINUOUS-FUNCTION-017 · ★★☆ Intermediate
If \(f\) and \(g\) are continuous at \(c\), which of these functions is always continuous at \(c\)?
Choose one option.
Show answer
- D. \(f+g\)
Explanation
The sum preserves continuity. The quotient fails if \(g(c)=0\), \(1/f\) if \(f(c)=0\), and \(f\circ g\) needs \(f\) continuous at \(g(c)\), not at \(c\).
Review the concept: Continuous function
A function \(f\) is continuous at \(a\) if \(f(a)\) is defined, its limit as \(x\) tends to \(a\) exists and equals \(f(a)\).
\[\lim_{x\to a}f(x)=f(a)\]
More practice problems: continuous function
- ZW-CONTINUOUS-FUNCTION-001 Which of the following is NOT a condition for f to be continuous at a?
- ZW-CONTINUOUS-FUNCTION-002 At which point is the function f(x)=(1)/(x-4) discontinuous?
- ZW-CONTINUOUS-FUNCTION-003 Which value of k makes f(x)=begincases(x^2-4)/(x-2)&if x≠22mm] k&if x=2endcases continuous at x = 2?
- ZW-CONTINUOUS-FUNCTION-004 Which value of k makes f(x)=begincasesx+1&if x<1\\ kx^2&if x≥1endcases continuous at x = 1?
- ZW-CONTINUOUS-FUNCTION-005 Which value of k makes f(x)=begincaseskx-3&if x≤2\\ x^2-1&if x>2endcases continuous at x = 2?
- ZW-CONTINUOUS-FUNCTION-006 Which value of k makes f(x)=(x^2-9)/(x-3) continuous at x = 3 when x≠3 and f(3)=k?
- ZW-CONTINUOUS-FUNCTION-007 Which value of k makes continuous at x = 1 the function defined by f(x)=x+k if x<1 and f(x)=2x^2 if…
- ZW-CONTINUOUS-FUNCTION-008 Which statement about the continuity of f at a point a is correct?