Let f : [0, \pi] \to R be defined as f(x)= {\\begin{array}{cc}\sin x{ &\end{array} ,\if x \is \irrational \and \x ∊ [0 ,\pi];\tan^2x{,} ,\if x \is \rational \and x ∊[0 ,\pi]. The number o f points in [0, π] at which the function f is continuous is

KVPY SX SB Exam 20141 Question Paper

Question : 11 of 120

Marks: +1, -0

Let

f : [0, π] →

R be defined as

f(x)= {\{\table \sin x{,} ,\if x \is \irrational \and \x ∊ [0 ,π];\tan^2x{,} ,\if x \is \rational \and x ∊[0 ,π].

The number o f points in [0, π] at which the function f is continuous is

Solution:

f(x)=\{\table \sin x, x∉Q;\tan ^2x ,x∈Q

if is continuou s at x = 0, π
so 2 points

\sinx = \tan^2x ⇒ \sin x(\cos^2x - \sin x) = 0

sin x = 0
x = 0, π

\sin^2x + \sinx- 1 = 0

\sinx={-1±√5}/2

\sinx={√5-1}/2\;\;2 \values

Total 4 points

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