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Let $f (x) = a x + b, x \in R, a n d g (x) = x + d, x \in R,$ then $f o g = g o f$ if and only if

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f(a)=g(c)

f(d)=g(b)

f(b)=g(d)

f(c)=g(a)

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detailed solution

Correct option is B

f(g(x))=g(f(x)) for all x∈R⇔f(cx+d)=g(ax+b)⇔ a(cx+d)+b=c(ax+b)+d⇔ad+b=cb+d⇔ f(d)=g(b)

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Let f(x)=ax+b, x∈R, and g(x)=x+d, x∈R, then fog=gof if and only if

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Let $f (x) = a x + b, x \in R, a n d g (x) = x + d, x \in R,$ then $f o g = g o f$ if and only if