Question
Download Solution PDFमाना कि f, g : R → R, f(x) = |x| + x और g(x) = |x| - x ∀ x ∈ R द्वारा परिभाषित दो फलन हैं। x < 0 के लिए (fog) (x) क्या है?
Answer (Detailed Solution Below)
Detailed Solution
Download Solution PDFअवधारणा:
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।
यहाँ g का प्रक्षेत्र R है और f का प्रांत भी R है इसलिए (fog) (x) परिभाषित किया गया है
फलन का संयोजन:
(fog) (x) = f[g(x)]
गणना:
दिया हुआ, f, g : R → R, f(x) = |x| + x और g(x) = |x| - x ∀ x ∈ R द्वारा परिभाषित दो फलन हैं।
दिया हुआ, x < 0
If(x) = |x| + x और g(x) = |x| - x
अभी, (fog) (x) = f[g(x)] = |g(x)| + g(x)
For x < 0, g(x) = - x + x = 0
⇒ (fog) (x) = f[g(x)] = |g(x)| + g(x)
= 0 + 0 = 0
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