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Consider the function f(x)={x2−1,2ax,amp;xamp;x≥3lt;3 for all real numbers x.If f is continuous at x=3, then the value of a is
- A.
8
- B.
3 / 4
- C.
1 / 8
- D.
4 / 3
(Correct Answer)
Explanation
**Concept:**
If a function f(x) is continuous at x=a, then
x→a+limf(x)=x→a−limf(x)=f(a)
**Calculation:**
x→3−limf(x)=32−1=8
x→3+limf(x)=2a(3)=6a
For continuity at x=3,
x→3−limf(x)=x→3+limf(x)
⇒8=6a
⇒a=34
Hence, value of a=34
Explanation
**Concept:**
If a function f(x) is continuous at x=a, then
x→a+limf(x)=x→a−limf(x)=f(a)
**Calculation:**
x→3−limf(x)=32−1=8
x→3+limf(x)=2a(3)=6a
For continuity at x=3,
x→3−limf(x)=x→3+limf(x)
⇒8=6a
⇒a=34
Hence, value of a=34
