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If (f:\mathbb{R}\to\mathbb{R}) and (g:\mathbb{R}\to\mathbb{R}) are given by (f(x)=3x+1) and (g(x)=x^2), what is ((g\circ f)(x))?यदि (f:\mathbb{R}\to\mathbb{R}) और (g:\mathbb{R}\to\mathbb{R}) इस प्रकार हैं कि (f(x)=3x+1) और (g(x)=x^2), तो ((g\circ f)(x)) क्या होगा?
Answer and explanationउत्तर और व्याख्या
Correct answer:सही उत्तर: (9x^2+6x+1)(9x^2+6x+1)
Step 1: ((g\circ f)(x)) means apply (f) first and then apply (g). Step 2: (g(f(x))=(3x+1)^2=9x^2+6x+1). Step 3: In composition, order matters; always simplify the inside function first.चरण 1: ((g\circ f)(x)) का अर्थ है पहले (f(x)) लगाएँ, फिर (g) लगाएँ। चरण 2: (g(f(x))=(3x+1)^2=9x^2+6x+1)। चरण 3: संयोजन में क्रम बहुत महत्त्वपूर्ण है, इसलिए पहले अंदर वाले फलन को हल करें।
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