Show that `f(x)={5x-4`, when `0ltxle1, 4x^3-3x` , when ` 1ltxlt2` is continuous at `x=1.`

Explanation

`lim _{x rightarrow 1^{+}} f(x)=lim _{x rightarrow 1^{+}}(4 x^{2}-3 x)=4(1)^{2}=4(1) `

`lim _{x rightarrow 1^{-}} f(x)=lim _{x rightarrow 1-}(5 x-4)=5(1)-4=1 . `

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

( hence porved)