Check sibling questions

If f (x) = 2x and g (x) = x^2/2+1 , then which of the following can be a discontinuous function

(A) f (x) + g (x)Β 

(B) f (x) – g (x)

(C) f (x) . g (x)Β 

(D) g(x)/(f(x))

This question is similar to Ex 5.1, 21 - Chapter 5 Class 12 - Continuity and Differentiability

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Transcript

Question 13 If f (x) = 2x and g (x) = π‘₯^2/2+1 , then which of the following can be a discontinuous function (A) 𝑓 (π‘₯) + 𝑔 (π‘₯) (B) f (x) – g (x) (C) 𝑓 (π‘₯) . 𝑔 (π‘₯) (D) 𝑔(π‘₯)/(𝑓(π‘₯)) Given functions 𝑓(π‘₯)=2π‘₯ & 𝑔(π‘₯)=π‘₯^2/2+1 Checking each option one by one Option 1 𝒇 (𝒙)+ π’ˆ (𝒙)=2π‘₯+π‘₯^2/2+1 =𝟏/𝟐 𝒙^𝟐+πŸπ’™+𝟏 Continuous since it is a polynomial function Option 2 𝒇 (𝒙)βˆ’ π’ˆ (𝒙)=2π‘₯βˆ’(π‘₯^2/2+1) =2π‘₯βˆ’π‘₯^2/2βˆ’1 =βˆ’πŸ/𝟐 𝒙^𝟐+πŸπ’™βˆ’πŸ Continuous since it is a polynomial function Option 3 𝒇 (𝒙)βˆ™π’ˆ (𝒙)=2π‘₯βˆ™(π‘₯^2/2+1) =(2π‘₯^3)/2+2π‘₯ =𝒙^πŸ‘+πŸπ’™ Continuous since it is a polynomial function Option 4 (π’ˆ(𝒙))/(𝒇(𝒙))=((π‘₯^2/2+ 1))/2π‘₯ =(((π‘₯^2 + 2)/2))/2π‘₯ =(𝒙^𝟐+𝟐)/πŸ’π’™ Not defined when 4π‘₯=0 i.e., 𝒙=𝟎 ∴ (𝑔(π‘₯))/(𝑓(π‘₯)) is a discontinuous function when π‘₯=0 So, the correct answer is (D)

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Davneet Singh

Davneet Singh is a graduate from Indian Institute of Technology, Kanpur. He has been teaching from the past 12 years. He provides courses for Maths and Science at Teachoo.