functions: If f(x) = x^2 + 18, f(2m) = 2f(m), what is m?

[Love21]

Let the function f be defined by f (x) = xsquared + 18
If m is a positive number such that f (2m) = 2f (m)
what is the value of m?

f(x) = xsquared + 18
f(2m) =2f (m)

How to continue? Thanks!!

 

[pka]

Re: functions

\(\displaystyle 2f(m) = 2\left( {m^2 + 18} \right)\;\& \; f(2m) = \left( {2m} \right)^2 + 18\)

 

[stapel]

f(x) = xsquared + 18
f(2m) =2f (m)

How to continue?

Continue by using the given information and solving the provided equation! :wink:

i) Plug "2m" in for "x" in the formula for f(x). Simplify.

ii) Plug "m" in for "x" in the formula for f(x). Multiply by 2, and simplify.

iii) Set (i) and (ii) equal.

iv) Solve the equation in (iii).

Have fun!

Eliz.