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Finding the transformation of a linear function $f(x)=mx+c$ to $af(bx)$.

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If $f(x)=\\simplify{{m}x+{c}}$, what is $\\simplify{{a}f({b}x)}$?

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To make the transformation from $f(x)=\\simplify{{m}x+{c}}$ to $\\simplify{{a}f({b}x)}$, we need to replace the $x$-terms in $f(x)$ with $\\simplify{{b}x}$, and then multiply this function by $\\var{a}$:

\n

{advice}

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\\\\[ \\\\begin{split} \\\\simplify{{a}f({b}x)} &\\\\,= \\\\simplify[!expandBrackets]{{a}({m}({b}x)+{c})} \\\\\\\\ &\\\\,=\\\\simplify[cancelTerms]{{a}({m*b}x+{c})}. \\\\end{split} \\\\]

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\\\\[ \\\\begin{split} \\\\simplify{{a}f({b}x)} &\\\\,= \\\\simplify[!expandBrackets]{{a}({m}({b}x)+{c})} \\\\\\\\ &\\\\,=\\\\simplify[!collectNumbers,!expandBrackets]{{a}({m*b}x+{c})}\\\\\\\\ &\\\\,= \\\\simplify[all, cancelTerms]{{a*simp}({m*b/simp}x+{c/simp})}. \\\\end{split} \\\\]

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$\\simplify{{a}f({b}x)}=$[[0]]

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