If the function `f(x)` given by `f(x)={3a x+b ,\ \ \ if\ x >1\ \ \ \ \ 11 ,\ \ \ \ \ \ \ \ \ if\ x=1 5a x-2b ,\ \ \ if\ x<1` is continuous at `x=-1` , find the values of `a` and `b` .

Explanation

Here f(x) is continuous at` x=1`


( L.H.L. of f(x) at `x=1`)=( R.H.L. of f(x) at `x=1)=f(1)`

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Rightarrow lim _{x rightarrow 1^{-}} f(x)=lim _{x rightarrow 1^{+}} f(x)=f(1)`

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lim _{x rightarrow 1^{-}} f(x)=lim _{x rightarrow 1} 5 a x-2 b[because f(x)=5 a x-2 f if x<1]`

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=5 a-2 b `

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