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Example 8 - Discuss continuity of f(x) = x3 + x2 - 1 - Examples

Example 8 - Chapter 5 Class 12 Continuity and Differentiability - Part 2

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Example 8 Discuss the continuity of the function f given by 𝑓 (π‘₯)= π‘₯3 + π‘₯2 βˆ’ 1.Given 𝑓(π‘₯)= π‘₯3 + π‘₯2 βˆ’ 1. To check continuity of 𝑓(π‘₯), We check it’s if it is continuous at any point x = c Let c be any real number f is continuous at π‘₯ =𝑐 if (π₯𝐒𝐦)┬(𝐱→𝒄) 𝒇(𝒙)=𝒇(𝒄) (π₯𝐒𝐦)┬(𝐱→𝒄) 𝒇(𝒙) = lim┬(x→𝑐) (π‘₯3 + π‘₯2 βˆ’ 1) Putting π‘₯=𝑐 = c3 +𝑐2 βˆ’ 1 𝒇(𝒄) =𝑐3 +𝑐2 βˆ’ 1 Since, L.H.S = R.H.S ∴ Function is continuous at x = c Thus, we can write that f is continuous for x = c , where c βˆˆπ‘ ∴ f is continuous for every real number.

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