+ m = 7 \implies m = 10.
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- Solution: Substitute $ x = 3 $ into $ f(x) $:
- f(3) = (3)^2 - 4(3) + m = 9 - 12 + m = -3 + m.
- Set this equal to 7:
- Question: A virologist studies the replication rate of a virus using the equation $ g(x) = x^2 - 4x + 3m $. If the replication rate at $ x = 2 $ equals the rate of a control sample modeled by $ f(x) = x^2 - 4x + m $, find $ m $.
- Solution: Compute $ g(2) $ and $ f(2) $:
- g(2) = (2)^2 - 4(2) + 3m = 4 - 8 + 3m = -4 + 3m,
