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Rasek [7]
2 years ago
11

For any linear function f(x) = mx + b, when does kf(x) = f(kx)?

Mathematics
1 answer:
iogann1982 [59]2 years ago
4 0

Only when <em>b</em> = 0 or <em>k</em> = 1<em>.</em>

If <em>f(x)</em> = <em>mx</em> + <em>b</em>, then

<em>f</em> (<em>kx</em>) = <em>m</em> (<em>kx</em>) + <em>b</em> = <em>mkx</em> + <em>b</em>

while

<em>k</em> <em>f(x)</em> = <em>k</em> (<em>mx</em> + <em>b</em>) = <em>kmx</em> + <em>kb</em>

The two expression are identical only if

<em>kb</em> = <em>b</em>   ===>   <em>kb</em> - <em>b</em> = 0   ===>   <em>b</em> (<em>k</em> - 1) = 0   ===>   <em>b</em> = 0 or <em>k</em> = 1

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