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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

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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