Math Help - Function notation problem

1. Function notation problem

Let the function f be defined by f(x)=5x-2a , where a is a constant. If f(10)+f(5)=55, what is the value of a?

How do you do this?

2. Er, never mind, figured it out. :P

3. Note that $f\left( 5 \right) = 55 - f\left( {10} \right)$.

But $f\left( 5 \right) = 5\left( 5 \right) - 2a = 25 - 2a$

This means that $55 - f\left( {10} \right) = 25 - 2a$. Which means that $f\left( {10} \right) = 30 + 2a$.

But $f\left( {10} \right) = 5\left( 10 \right) - 2a = 50 - 2a$.

You can solve for $a$ from the last two equations.

What did you get?

4. Originally Posted by guildmage
Note that $f\left( 5 \right) = 55 - f\left( {10} \right)$.

But $f\left( 5 \right) = 5\left( 5 \right) - 2a = 25 - 2a$

This means that $55 - f\left( {10} \right) = 25 - 2a$. Which means that $f\left( {10} \right) = 30 + 2a$.

But $f\left( {10} \right) = 5\left( 10 \right) - 2a = 50 - 2a$.

You can solve for $a$ from the last two equations.

What did you get?
5.

5. That's correct.