ramanwaterfalls2259 ramanwaterfalls2259
  • 11-10-2021
  • Mathematics
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For any linear function f(x) = mx + b, when does kf(x) = f(kx)?

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LammettHash
LammettHash LammettHash
  • 11-10-2021

Only when b = 0 or k = 1.

If f(x) = mx + b, then

f (kx) = m (kx) + b = mkx + b

while

k f(x) = k (mx + b) = kmx + kb

The two expression are identical only if

kb = b   ===>   kb - b = 0   ===>   b (k - 1) = 0   ===>   b = 0 or k = 1

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