Question
Download Solution PDFयदि f(y) = (y)[y] है, जहाँ [.] सबसे छोटा पूर्णांक फलन को दर्शाता है और g(y) = y2 है, तो g o f(- 3/2) का मान ज्ञात कीजिए।
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सबसे छोटा पूर्णांक फलन:
फलन f (x) = [x] को सबसे छोटा पूर्णांक फलन कहा जाता है और इसका अर्थ है कि सबसे छोटा पूर्णांक x से अधिक या उसके बराबर है अर्थात् [x] ≥ x है।
सबसे छोटे पूर्णांक फ़लन के लिए ग्राफ नीचे दिया गया है,
गणना:
दिया गया है: f(y) = (y)[y] है, जहाँ [.] सबसे छोटे पूर्णांक फलन को दर्शाता है और g(y) = y2 है।
यहाँ, हमें g o f(- 3/2) का मान ज्ञात करना है।
⇒ g o f(- 3/2) = g( f(- 3/2))
∵ f(y) = (y)[y] जहाँ [.] सबसे छोटे पूर्णांक फलन को दर्शाता है
⇒ f(- 3/2) = (-3/2)[- 3/2]
चूँकि हम जानते हैं कि, [- 3/2] = - 1
⇒ f(- 3/2) = (- 3/2)-1 = - 2/3
⇒ g o f(- 3/2) = g(-2/3)
∵ g(y) = y2 इसलिए, g(-2/3) = (-2/3)2 = 4/9
अतः g o f(- 3/2) = 4/9
Last updated on Jun 19, 2025
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