<p>Let the function f and g be defined by f(x) = x+3 and g(2x) = 2(fx). If g(2m) = g(m) +10, what is the value of m?</p>
<p>A)4
B)6
C)8
D)10
E)20</p>
<p>Here is how far I have gotten</p>
<p>since 2(fx) means 2(x+3) = 2x+6</p>
<p>I am lost after this. :/</p>
<p>answer is D and please explain</p>
<p>Let the function f and g be defined by f(x) = x+3 and g(2x) = 2*f(x). If g(2m) = g(m) +10, what is the value of m?</p>
<p>First solve for all the functions:
f(x) = x + 3;
g(2x) = 2*f(x);
g(2m) = 2(m+3);
g(m) + 10 = 2(m/2+3) + 10;</p>
<p>Now set them equal to one another:
2m+6 = m+16;
m = 10;</p>
<p>g(m) + 10 = 2(m/2+3) + 10;</p>
<p>I am lost at that step</p>
<p>Why do you have (m/2) and where did you get it from?</p>
<p>g(2x) = 2<em>f(x+), correct?
Therefore:
g(x) = 2</em>f(x/2), do you follow?
Now we’re plugging in m where x is, so we have:
g(m) = 2*(m/2+3) + 10;
Now multiply the inside stuff by the outside 2:
g(m) = m + 6 + 10;
Finally add the constants together:
g(m) = m + 16;
And there you have it, the second equation.</p>
<p>I get it. Omg thank you.</p>
<p>Yay glad I could help!</p>
<p>I just looked for a pattern in g(anything) = something</p>
<p>Use 1 for x: g(2x) = g(2) = 2(f(1)) = 8
Use 2 for x: g(2x) = g(4) = 2(f(2)) = 10</p>
<p>If you want more, then do it, but there is a pattern here: The resultant number inside g() is always equal to a number 6 more than itself; 2->8, 4->10; So, we can start plugging and trying numbers from the answer choices to see when g(2m) is equal to a number 6 greater than it.</p>
<p>10 works, in this case, while the others don’t:
g(2(10)) = g(20) = g(10) + 10 = 16 + 10 = 26 = g(20)
Notice, 26 is bigger than the resultant number, 20, inside g().</p>
<p>This is obviously not as elegant as the previous explanation but it worked for me really quickly and well, and it might for you too.</p>