Exercise · ZW-CONTINUOUS-FUNCTION-002 · ★☆☆ Basic
At which point is the function \(f(x)=\dfrac{1}{x-4}\) discontinuous?
Choose one option.
Show answer
- D. x = 4
Explanation
The function is undefined at x = 4 (the denominator vanishes), so there f(4) does not exist. Everywhere else on the real line it is continuous.
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?
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- 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?
- ZW-CONTINUOUS-FUNCTION-009 What type of discontinuity does f(x)=(x^2-1)/(x-1) have at x = 1?