If f(x) = ax + b and g(x) = cx + d,then f(g(x | vedclass

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(C) Given $f(x) = ax + b$ and $g(x) = cx + d$.We are given the condition $f(g(x)) = g(f(x))$.First,calculate $f(g(x)) = f(cx + d) = a(cx + d) + b = ac

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$f(d) = g(b)$

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(C) Given $f(x) = ax + b$ and $g(x) = cx + d$.We are given the condition $f(g(x)) = g(f(x))$.First,calculate $f(g(x)) = f(cx + d) = a(cx + d) + b = acx + ad + b$.Next,calculate $g(f(x)) = g(ax + b) = c(ax + b) + d = cax + cb + d$.Equating the two expressions: $acx + ad + b = cax + cb + d$.Since $acx = cax$,we can cancel these terms from both sides:$ad + b = cb + d$.Rearranging the terms,we get $ad + b = cb + d$.Note that $f(d) = ad + b$ and $g(b) = cb + d$.Therefore,the condition $f(g(x)) = g(f(x))$ is equivalent to $f(d) = g(b)$.

If $f(x) = ax + b$ and $g(x) = cx + d$,then $f(g(x)) = g(f(x))$ is equivalent to

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