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  • The function <img alt="\mathrm{f(x)=a[x+1]+b[x-1],(a \neq 0, b \neq 0 ) }" src="https://entrancecorner.oncodecogs.com/gif.latex?%5Cmathrm%7Bf%28x%29%3Da%5Bx&plus;1%5D&plus;b%5Bx-1%5D%2C%28a

The function \mathrm{f(x)=a[x+1]+b[x-1],(a \neq 0, b \neq 0 ) }where [x] is the greatest integer function is continuous at x=1 if
 

Option: 1

a=2 b
 


Option: 2

a=b
 


Option: 3

a+b=0
 


Option: 4

a+2 b=0


Answers (1)

best_answer

\mathrm{f(1)=2 a, \lim _{x \rightarrow 1_{-}} f(x)=a-b ~so~ a+b=0 \text{for f to be continuous at x=1.}}

Posted by

sudhir.kumar

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