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let f(x)={x^2+ax+b, 0ltxlt2 and 3x+2 , 2...

let `f(x)={x^2+ax+b, 0ltxlt2 and 3x+2 , 2lexlt4 and 2ax+5b , 4lexlt8 `. if f(x) is continuous on close interval`(0,8) `.find value of` a and b.`

Text Solution

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Here, value of `f(x)` is changing at `2` and `4`.
So, `f(x)` to be continuous,
`f(2^-) = f(2^+)`
`=>2^2+2a+b = 3(2)+2`
`=>4+2a+b = 8`
`=>2a+b = 4->(1)`
Also, `f(x)` to be continuous,
`f(4^-) = f(4^+)`
...
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