ATAR Notes: Forum

VCE Stuff => VCE Mathematics => VCE Mathematics/Science/Technology => VCE Subjects + Help => VCE Mathematical Methods CAS => Topic started by: Sanguinne on March 26, 2013, 05:35:18 pm

Title: anyone know how to solve???
Post by: Sanguinne on March 26, 2013, 05:35:18 pm: ok so this is the question

f:R-->R, f(x)=mx-4 where m ∈ R\{0}

a) find the x-axis intercept
b)for which values of m is the x-axis intercept less than or equal to 1?
c) find the inverse function of f
d) find the coordinates of the point of intersection of the graph y=f(x) with the graph of y=x
e) find the equation of the line perpendicular to the line at the point with coordinates (0,-4)
Title: Re: anyone know how to solve???
Post by: Zealous on March 26, 2013, 06:23:49 pm: I've got an idea on how to solve most of it, although someone else should probably check with my working, I may not be fully correct.

a)
x-axis intercept,
when $f(x) = 0$

$mx - 4 = 0$

$mx = 4$

$x =$ ${4}\over m$

b)
usng values from previous question:
$4\over m$ $\leqslant 1$

so $4\leqslant m$

c)
for the inverse: swap x and y values
$x = my - 4$

$x + 4 = my$

$y =$ $(x+4)\over m$

e)
the gradient of the line is $m$
so the gradient of the perpendicular line will be $-$ $1 \over m$

using the formula $y - y_1 = m(x - x_1)$

sub in the coordinates:
$y - (-4) =$ $-$ $1 \over m$ $(x - 0)$

$y + 4 = -$ $x \over m$

$y = -$ $x \over m$ $-4$

I'm having a few problems with d though...
Title: Re: anyone know how to solve???
Post by: Homer on March 26, 2013, 06:52:12 pm: Quote from: Sanguinne on March 26, 2013, 05:35:18 pm
ok so this is the question

f:R-->R, f(x)=mx-4 where m ∈ R\{0}

d) find the coordinates of the point of intersection of the graph y=f(x) with the graph of y=x

$x=mx-4$
$(\frac{-4}{1-m},\frac{-4m}{1-m}-4)$
Title: Re: anyone know how to solve???
Post by: Zealous on March 26, 2013, 06:53:52 pm: Quote from: Homer on March 26, 2013, 06:52:12 pm
$x=mx-4$
$(\frac{-4}{1-m},\frac{-4m}{1-m}-4)$

How did you get x by itself after equating them?
Title: Re: anyone know how to solve???
Post by: KevinooBz on March 26, 2013, 07:01:50 pm: Quote from: Ovazealous on March 26, 2013, 06:53:52 pm
How did you get x by itself after equating them?
You move mx to the other side and you factorise by taking out x then divide by (1-m).
Title: Re: anyone know how to solve???
Post by: Sanguinne on March 26, 2013, 07:54:06 pm: thanks everyone for ur answers

really helpful ;D