<p>I am alright at basic function problems, but with I get confused when they get a little more complex like this:</p>
<p>Let the function f be defined by f(x) = x^2 + 18. If m is a positive number such that f(2m) = 2f(m), what is the value of m? </p>
<p>No idea how to solve that. Any tips on function questions?</p>
<p>f(x) = x^2 + 18</p>
<p>f(2m) = 2 f(m)
(2m)^2 + 18 = 2 [ m^2 + 18 ]
4 m^2 + 18 = 2 m^2 + 36
2 m^2 = 18
m^2 = 9
m = 3, -3</p>
<p>Edit: Since m is positive, m=3.</p>
<p>This problem just reduces to an equation with a single variable x.</p>
<p>Substitute '2m' for 'x' in f(x), to get f(2m);
f(2m) = (2m)^2 + 18 = 4m^2 + 18</p>
<p>Similarly, substitute 'm' for 'x' in f(x), to get f(m):
f(m) = m^2 + 18</p>
<p>f(2m) = 2f(m), or 4m^2 + 18 = 2( m^2 + 18) or 2m^2 + 36
4m^2 - 2m^2 = 36 - 18
2m^2 = 18
m^2 = 9
m = +/- 3</p>
<p>Since m is positive, m=3 ( I missed this, first time through...)</p>