You are Here: Home >< Maths

# C3 (AEA Ext.) Proof of functions watch

Announcements
1. Given that , show that,
a) if f(x) is an even function, then and hence , where k is constant.

I can show that ad=bc, since when the function is even, however I become stuck trying to prove that there will be a constant.

Would it be that for ax+b/cx+d to be even, that a and c must be 0? Therefore ad=bc=0 but b and d can be any value, leaving just a constant or is there another way to show this?
2. (Original post by TheTallOne)
Given that , show that,
a) if f(x) is an even function, then and hence , where k is constant.

I can show that ad=bc, since when the function is even, however I become stuck trying to prove that there will be a constant.
Why does when the function is even?

Would it be that for ax+b/cx+d to be even, that a and c must be 0? Therefore ad=bc=0 but b and d can be any value, leaving just a constant or is there another way to show this?
No. What happens if a=b=c=d=1?
3. Sorry, it's f(x)=f(-x)

and I could add if a=c and b=d
4. Think about it the other way: What does it mean for to be a constant k? (i.e. what does that tell you about a,b,c,d)?
5. That the coefficient of x must be 0 when ax+b/cx+d is simplified.
6. (Original post by TheTallOne)
That the coefficient of x must be 0 when ax+b/cx+d is simplified.
That's true, and it's one way of finding an answer. But to a large extent I think you're going in circles here - if you couldn't see how to answer the question before, I'm not sure you'll be able to now.

I was more thinking that if you know , then what's the obvious thing to do next?

7. ???
Sorry- I went for lunch.
8. You're expecting it to be true for all x, so trying to solve for x isn't a terribly good plan.

You have , and this is true for all x.

So what happens when x= 0?
What happens when x=1? (Given what you learned from looking at x=0).

Of course, this is all arguing backwards from the answer, so you now have to adapt your reasoning so that you are arguing forwards from ad = bc. (Hint for that: work out what k must be first).

9. When x=1,

So

Goes to....
a=bc/d

Thanks

TSR Support Team

We have a brilliant team of more than 60 Support Team members looking after discussions on The Student Room, helping to make it a fun, safe and useful place to hang out.

This forum is supported by:
Updated: July 19, 2007
Today on TSR

Choose Respect

### University open days

• Manchester Metropolitan University
Wed, 14 Nov '18
• University of Chester
Wed, 14 Nov '18
• Anglia Ruskin University
Ambitious, driven, developing your career & employability? Aspiring in your field, up-skilling after a career break? Then our Postgrad Open Evening is for you. Postgraduate
Wed, 14 Nov '18
Poll
Useful resources

### Maths Forum posting guidelines

Not sure where to post? Read the updated guidelines here

### How to use LaTex

Writing equations the easy way

### Study habits of A* students

Top tips from students who have already aced their exams