Questions thread

[kenhung123]

Yep just factorise the x and then divide both sides

[Hielly]

why does the answer say f^-1(x) = x+1/x-1 ?

[kenhung123]

Opps sorry I mean factorise y. Yep that is right.

[Hielly]

hrmm i dont quite get it, can someone do the first question?

thanks

[Stroodle]

[Ilovemathsmeth]

Hielly, the first question about finding the inverse where there are two x variables - I used to divide the numerator by the denominator using long division to get it into the more standard hyperbolic form. It works well and allows you to find the inverse from there.

It's a quadratic. So that means you need to graph it, to solve some of the inequalities or you can use the modulus method described earlier in this thread/or another thread. Think of it like this. The above graph needs to be greater than the line y = x etc. Which part were you having difficulty with?

[Hielly]

hey
yeah i understand now. thanks

thanks
also not sure what equation this is to sub in the points, how can you tell?

edit: wrong q attached before. this is the right one!

[kenhung123]

Use the general formula a(x-h)+k
y=a(x-4)+3 sub in (0.1) to find a

[Hielly]

yeah i used that too, but apparently the formula is -y=ax^2 + x + c for the left curve and y=ax^2 + x+ c for the right curve

[m@tty]

You have two points for each curve, sub these into the general form [as they specified coefficient of 'x' is 1]. You can find 'c' by subbing the y-int then find 'a' by subbing the other point on each curve.

[Hielly]

yeah i did that but why couldn't we use a(x-h)+k. Is it because the TP is unknown?

[m@tty]

For the left one you don't know turning point. And they specified that the coefficient of 'x' was 1.

[kenhung123]

yeah i used that too, but apparently the formula is -y=ax^2 + x + c for the left curve and y=ax^2 + x+ c for the right curve

As in the answer or form? You can just expand the (h,k) form to make it like that

[m@tty]

Why bother expanding it like that if you can put it straight into the required form??

As they have specified the coefficient of 'x' is 1 this implies Wait...This actually works out nicely.

You can do this for the other as well as you know the x co-ord of the t.p. [line of symmetry] at


Then you can sub the y-intercepts in to find 'c'.

I was going to say just sub into general form as they stated that, but this works out easier.

[Hielly]

thanks

also for this Q.

how would you sketch b) and for c) what impact does 18 and -2 have on the graph?

thanks