If $f(a*b)=f(a)+f(b)$ , what is the value of $f(1)$ ?

Correct answer marked below

1

-1

0

Correct

2

-2

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Explanation

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Comments

IhazSep 11

Got it! Plugged in a=b=1 and it clicked. Thanks!

AnuSep 18

Same here, such a neat trick!

NurmuhammadMay 25

Why can't we just plug in a=1, b=0? I got confused because f(0) isn't given. Anyone else?

ChiJun 8

Because the equation is only given for multiplication, and 0 times anything is 0. You'd get f(0)=f(1)+f(0) which doesn't help. Stick with 1*1.

SanyaJul 17

This is a classic functional equation. For anyone stuck: set a=b=1. That gives f(1)=f(1)+f(1), so f(1)=0. Easy once you see it.

AnanyaJul 17

Medium difficulty. I initially tried a=2, b=1 but that led nowhere. The 1*1 substitution is key. Good practice for function problems!

PulkitJul 29

Yeah, I did the same at first. It's tricky because you have to think about what values make the equation simplify.

ShwetaJul 31

Exactly! And it's a reminder to always try the simplest numbers first.

What this question tests

Your ability to evaluate and compose functions, including unusual defined operations.

Applying function operations in the wrong order or ignoring domain restrictions.

If f(a∗b)=f(a)+f(b)f(a*b)=f(a)+f(b)f(a∗b)=f(a)+f(b), what is the value of f(1)f(1)f(1)?