Question
Download Solution PDFयदि f(x) = 4x + 1 और g(x) = kx + 2 इस प्रकार है कि fog(x) = gof(x) है, तो k का मान क्या है ?
Answer (Detailed Solution Below)
Detailed Solution
Download Solution PDFव्याख्या:
दिया गया है: f(x) = 4x + 1 और g(x) = kx + 2 जैसा कि fog(x) = gof(x)
fog(x) = f(g(x)) = 4g(x) + 1
⇒ fog(x) = 4(kx + 2) + 1 = 4kx + 9 __-(i)
और gof(x) = g(f(x)) = kf(x) + 2
⇒ gof(x) = k(4x + 1) + 2 = 4kx + k + 2 __(ii)
चूँकि fog(x) = gof(x), इसलिए (i) और (ii) को बराबर रखने पर,
⇒ 4kx + 9 = 4kx + k + 2
⇒ 9 = k + 2
⇒ k = 7
∴ सही विकल्प (1) है।
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