1.

Find the values of a and b such that the function defined by `f(x)={{:(5, if xle2), (a x+b , if 2 lt x lt10 ),(21 , ifx ge10):}` is a continuous function.

Answer» Here, value of `f(x)` is changing at `x = 2` and `x = 10`.
So, `f(x)` to be continuous,
`f(2^-) = f(2^+)`
`=>5 = a(2)+b`
`=>2a+b = 5->(1)`
Also, `f(x)` to be continuous,
`f((10^-) = f(10^+)`
`=>a(10) + b = 21`
`=>10a+b = 21->(2)`
Subtracting (2) -(1),
`=>10a+b-2a-b = 21-5`
`=>8a = 16`
`=> a= 2`
`:. 2(2)+b = 5`
`=>b = 1`
`:.` For, `a = 2, b =1, f(x)` will be continuous.


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