Find the values of a and b such that the function defined by `f(x)={5, ifxlt=2a x+b , if2

Explanation

At x =2
`f(2) = 5`
L.H.L. `underset(x to 2^(-))(lim)f(x)=underset( h to 0)(lim) f(2-h)= underset(hto 0)(lim) 5-5 `
R.H.L.
`underset(x to 2^(+))(lim)f(x)=underset( h to 0)(lim) f(2+h)`
`underset(h to 0 )(lim)a (2 + h) + b 2a + b `
`:'` f(x) is continuous at x = 2 ...(i)
`:.` 2a + b = 5.
at x = 10
`f`(10) = 10 +b
R.H.L. `underset(x to 10^(+))(lim)f(x)=underset( h to 0)(lim) f(10+h)`
`underset(h to 0 )(lim)21 = 21`
`:'` f(x) is continous at x = 10
`:'` 10a +b = 21 ...(2)
From equation (1) and (2)
a = 2, b = 1