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Question

f(x) = 6x^2 -12x +1 and g(x) = -x+c

given that (gof)(x) ≤ 0, for x is all real numbers, find the values for c

Answer 1

(g•f)(x) = - 6x² + 12x - 1 + c ≤0; discriminant d = 12² - 4(-6)(- 1 + c) = 0; 144 - 24 + 24c = 0; c = - 120/24 = - 5