<p>A certain function f has the property that f (x + y) = f(x) + f(y) for all values of x and y. Which of the following must be true when a=b</p>
<ol>
<li><p>f(a+b) = 2 f(a)</p></li>
<li><p>f (a+b) = (f(a))^2</p></li>
<li><p>f(b) + f(b) = f(2a)</p></li>
</ol>
<p>I know that One must be true and 2 is false, but why is 3 true? Can you also provide an example of a function like that?</p>
<p>Function is my weakest area in math sat, but I think substitution does the trick.</p>
<p>f=5
a=4
b=3</p>
<p>A works and B doesn’t, as you know, so let’s try C.</p>
<p>5(3) + 5(3) = 5(2x4)</p>
<p>Boom.</p>
<p>^ why are you giving f a value? Well I’ve never taken an SAT but suppose x=a and y=b, so like stated a=b then x must=y. </p>
<p>Assume x and y (a and b) are both 1. The first two are correct as you said. </p>
<p>So,
f(1)+f(1)=f(2(1))
1+1=2
2=2</p>
<p>That’s the way I would work it anyway lol.</p>
<p>Three is true because…</p>
<p>f(b) + f(b) = f(a) + f(a) , since a = b.</p>
<p>But f(a)+f(a) = 2 f(a). And since you already know that the 1st property is true, you can replace 2f(a) with f(2a). </p>
<p>As for a function with these properties, I believe that they are all true for any linear function that passes through the origin, f(x) = kx. But that information doesn’t really affect the solution.</p>