Question
Download Solution PDFअगर f(x) = 2|x| और g(x) = [x] जहां [.] महत्तम पूर्णांक फलन दर्शाता है तो f o g (- 17/2) का मान ज्ञात कीजिए।
Answer (Detailed Solution Below)
Detailed Solution
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महत्तम पूर्णांक फलन: (तल फलन)
फलन f(x) = [x] को महत्तम पूर्णांक फलन कहा जाता है और इसका मतलब है कि x से कम या उसके बराबर महत्तम पूर्णांक यानी [x] ≤ x।
[x] का डोमेन R है और परिसर I है।
यदि f :A → B और g : C → D है तो (fog) (x) केवल तब मौजूद होगा यदि g का सह-डोमेन = f का डोमेन अर्थात् D = A है और (gof) (x) केवल तब मौजूद होगा यदि f का सह-डोमेन = g का डोमेन अर्थात् B = C है।
गणना :
दिया गया है: f(x) = 2|x| और g(x) = [x] जहां [.] महत्तम पूर्णांक फलन दर्शाता है
यहाँ हमें f o g (- 3/2) का मान ज्ञात करना है
⇒ f o g (- 17/2) = f( g(- 17/2))
∵ g(x) = [x], इसलिए g(- 17/2) = [- 17/2] = - 9
⇒ f o g(- 17/2) = f(- 9)
∵ f(x) = 2|x| इसलिए f(- 9) = 2|- 9| = 29 = 512
अतः f o g (- 17/2) = 512
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