Then, f is
[JEE Main Online Paper (Held On 09-Jan-2019 Morning]
A) continuous if \[a=0\] and \[b=5\]
B) continuous if \[a=-5\] and \[b=10\]
C) continuous if \[a=5\] and \[b=5\]
D) not continuous for any values of a and b
Correct Answer: D
Solution :
For f to be continuous at \[x\,\,=\,\,1\] \[f({{1}^{-}})\,\,\,\,\,\,\,\,=\,\,\,\,f({{1}^{+}})\] \[5\,\,=\,\,a\,\,+\,\,b\] ..... (1) For f to be continuous at \[x\,\,=\,\,3\] \[f({{3}^{-}})\,\,=\,\,f({{3}^{+}})\] \[a+3b=b+15\] \[a+2b=15\] ..... (2) From (1) & (2) \[5+b=15\] \[b=10\text{ }\And \text{ }a=-5\] For f to be continuous at \[x\text{ }=\text{ }5\] \[f({{5}^{-}})\,\,=\,\,f({{5}^{+}})\] \[b+25=30\] \[b\text{ }=\text{ }5\] not continuous
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