SOLUTION: given the function f(x) = 4x^2 -4x +1 a. find f(1/2) b. find f(3b-1) Thanks so much

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Question 693743: given the function f(x) = 4x^2 -4x +1
a. find f(1/2)
b. find f(3b-1)

Thanks so much
Answer by RedemptiveMath(80) (Show Source):
You can put this solution on YOUR website!
1. f(1/2)

All we need to do is plug what is inside the parentheses after f into the places where x are and solve. So, with the function f(x) = 4x^2 - 4x + 1:

f(x) = 4x^2 - 4x + 1
f(1/2) = 4(1/2)^2 - 4(1/2) + 1
f(1/2) = 4(1/4) - 4(1/2) + 1
f(1/2) = 1 - 2 + 1
f(1/2) = 2 - 2 = 0.

f(1/2) = 0.

2. f(3b-1)

Again, we just plug (3b-1) into the places where x are:

f(x) = 4x^2 - 4x + 1
f(3b-1) = 4(3b-1)^2 - 4(3b-1) + 1
f(3b-1) = 4[(3b-1)(3b-1)] - 4(3b-1) + 1
f(3b-1) = 4(9b^2-6b+1) - 12b - 4 + 1
f(3b-1) = 36b^2 - 24b + 4 - 12b - 4 + 1
f(3b-1) = 36b^2 - 36b + 1.