Example 10 - Discuss continuity f(x) = {x+2, if x<1 x-2, if x>1 - Examples

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  1. Chapter 5 Class 12 Continuity and Differentiability
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Example 10 Discuss the continuity of the function f defined by 𝑓(π‘₯)={β–ˆ(&π‘₯+2, 𝑖𝑓 π‘₯≀1@&π‘₯βˆ’2, 𝑖𝑓 π‘₯>1)─ Given 𝑓(π‘₯)={β–ˆ(&π‘₯+2, 𝑖𝑓 π‘₯≀1@&π‘₯βˆ’2, 𝑖𝑓 π‘₯>1)─ The function is defined at All points of the Real line. Case 1 Checking continuity at x = 1 f is continuous at x = 1 if, L.H.L = R.H.L = 𝑓(1) i.e. lim┬(xβ†’1^βˆ’ ) 𝑓(π‘₯)=lim┬(xβ†’1^+ ) 𝑓(π‘₯)=𝑓(1)

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