<p>Alright well usually I'm pretty good with functions and I probably am just overthinking things but here are some difficult questions I need help with:</p>
<p>(x-8)(x-k) = x^2 -5kx + m</p>
<p>In the equation above, k and m are constants. If the equation is true for all values of x, what is the value of m?</p>
<p>The answer is 16. </p>
<p>Also, if f(x + y) = f(x) + f(y) for all values x and y, the following statement is true if a=b.</p>
<p>f(b) + f(b) = f(2a)</p>
<p>Why is this statement true?</p>
<p>Thanks for the quick help!</p>
<p>Actually lol I think I just got the second one:</p>
<p>f(b) + f(b) = f(a) + f(b) according to function rules. Therefore:</p>
<p>f(a) + f(b) = f(2a)</p>
<p>f(a) + f(b) = f(a + a)</p>
<p>f(a) + f(b) = f(a + b) <—This is essentially a restatement of the rules w/ original function.</p>
<p>Right? And I still need help with that first one :)</p>
<p>For the second question, yes you are correct because f(a+b)= f(a) +f(b), since a=b, it can also be written as f(b+b)= f(b) +f(b), so f(b+b) is equal to f(2b) or f(2a) as they are interchangeable.</p>
<p>For the first one, if you factor x^2 -5kx + m (since it’s a quadratic equation) you must get (x-8)(x-k). This means that 8+K=5K and 8K=m if you solve for K in the first one, K=2. If you plug that into 8K=m, you get 8(2)=16.</p>
<p>EDIT: The roots of the equation are +K and +8, that’s how you know their sum equals the constant of the second term (-5k) and their product equals the 3rd term (m)</p>
<p>Oh, I understand now! Thanks! Still seems a little advanced for a SAT question though lol</p>