If , what is the value of ?
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This one took me a minute to see. The trick is that you have to plug in both x and -x to get a system. Once I did that it was smooth.
Right, I was staring at it trying to isolate f(x) with just one equation at first lol.
Same. The symmetry is the whole point of these function problems.
Wait, when I substitute x = -1, I get 2f(-1) + 3f(1) = -15. Then with x = 1 I get 2f(1) + 3f(-1) = -5. Is that the right setup? I keep getting a weird value for f(1).
Yeah that's the setup, just solve the system. Your second equation looks right to me.
Good question but definitely on the easier side of this range once you spot the trick. I'd say 650ish.
Agreed, the algebra itself is simple, it's just recognizing you need two equations.
Idk, I overthought it and wasted too much time. Could see it tripping people up.
Thanks, this cleared up the approach for me. Been struggling with these functional equations.
What it tests
Your ability to evaluate and compose functions, including unusual defined operations.
Common trap
Applying function operations in the wrong order or ignoring domain restrictions.