` f(x){{:(10^(3) - 1"," if x le 1 ),(x^(2) "," if x gt 1 ):}`

Explanation

` f(x){{:(x^(10) - 1"," if x le 1 ),(x^(2) "," if x gt 1 ):}`
If x `lt` then f(x) = `x ^(10) -1` is a polynomial function.
If `x gt 1 then f(x) = x^(2)` is a monomial function.
A polynomial function is always continuous.
at x - 1
` f(1) = 1^(10) - 1 = 1= 1 -1 = 0 `
R.H.L = ` underset (x to 1^(+))(lim)f(x)`
Let 1 + h = x
`rArr 1 + h to 1`
`rArr h to 0 `
`=underset (h to 0)(lim) f(1+h)`
`=underset (h to 0)(lim) (1 - h)^(2) = ( 1+ 0)^(2)=1 `
`:'` f(1) `ne` R.H.L
`:.` therefore, f (x) is discontinuous at x = 1 only .