Question

Let 𝑓(𝑥) = {(2𝑥^2−3𝑥+1)/2𝑥−1, 𝑥 < 0.5

𝐴𝑥 + 𝐵, 𝑥 = 0.5
2𝐵, 𝑥 > 0.5}

Determine constants 𝐴 and 𝐵 such that are continuous for all
values of 𝑥. Show your work using the conditions of
continuity.

Thank you!

Answer 1

Assuming the usual carelessness with parentheses, I'll assume

f(x) = (2𝑥^2−3𝑥+1)/(2𝑥−1) = x-1 for x < 1/2
that means we need 2B = -1/2, B = -1/4
so
1/2 A + B = -1/2
1/2 A - 1/4 = -1/2
A = -1/2