Sophie Schmieg on Nostr: nprofile1q…targs Let's see: in order to have a solution, g needs to be linear, i.e. ...
nprofile1qy2hwumn8ghj7un9d3shjtnddaehgu3wwp6kyqpqzdp33shl69xr0uq3x8n5gsjykq9upycwh6nqm02c3f6x0frrn0dqftargs (nprofile…args)
Let's see: in order to have a solution, g needs to be linear, i.e. g(x) = ax + b
Substituting, we get:
f(g(x)) = a²x² + 2abx + b² - 2ax - 2b = a²*x² + (2ab - 2a)*x - 2b + b²
Comparing coefficients, this means:
a² = 4 => a = 2
2ab - 2a = -8 => 4b - 4 = -8 => b = -1
b² - 2b = 3 => b = 1 ± 2 confirms b = -1
g(x) was 2x - 1
Let's see: in order to have a solution, g needs to be linear, i.e. g(x) = ax + b
Substituting, we get:
f(g(x)) = a²x² + 2abx + b² - 2ax - 2b = a²*x² + (2ab - 2a)*x - 2b + b²
Comparing coefficients, this means:
a² = 4 => a = 2
2ab - 2a = -8 => 4b - 4 = -8 => b = -1
b² - 2b = 3 => b = 1 ± 2 confirms b = -1
g(x) was 2x - 1