A few days ago
Problems w/ function notation?
I did try….for a long time but I need guidance….Please explain why too.
“THe roots of the equation f(x)=0 are 1 and -2. The roots of f(2x)=0 are?
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A few days ago
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The roots of f(x) = 0 are 1 and -2. This means that x = 1 and x = -2 for f(x), which means that:
f(x) = (x – 1)(x + 2) = 0
Now expand the expression, (x – 1)(x + 2) to get:
f(x) = x^2 + 2x – x – 2
Therefore, f(x) = x^2 + x – 2.
To find f(2x), replace ‘x’ with ‘2x’ in f(x):
f(x) = x^2 + x – 2
=> f(2x) = (2x)^2 + (2x) – 2
Therefore, f(2x) = 4x^2 + 2x – 2.
To find the roots of f(2x), let f(2x) = 0, and factor the expression:
f(2x) = 0
=> 4x^2 + 2x – 2 = 0
=> 2(2x^2 + x – 1) = 0
=> 2(2x – 1)(x + 1) = 0
=> 2x – 1 = 0 and x + 1 = 0
=> x = 1/2 and x = -1
Therefore, the roots of f(2x) are: x = 1/2 and x = -1.
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