Functions

x --->(x3)-->(-3)-->y
a) Write down the output y in terms of x
b) Work out the output when the input is 10
c) Work out the value of x in terms of y
d) Sasha says, 'There is a value of x where is is equal to y'
Show that Sasha is correct

Book answers;
a) y=3x-3
b) 27
c) x=(y+3)/3
d)if x = y then x = 3x - 3
2x = 3, x=3/2(or 1.5)
Substituting x = 1.5 into the function,
y=1.5 x 3 - 3 = 1.5 = 3/2
So x and y can be equal.

My question:
Can anyone explain how they got 2x =3 ?
x = 3x - 3
I would assume you have to add x to both sides first, so it would be:
x + 3 = 3x
then i'd have to divide by 3:
(x+3)/3 =x
Not sure what else I can do to get get x = x
Source: Scholastic GCSE Foundation Mathematics: Page 72

(edited 3 years ago)

Reply 1

DianaJ22702

x = y
3x - 3 = y
Substitute x into y
3x - 3 = x
2x - 3 = 0
2x = 3
x = 3/2 or 1.5

Hope this helps :smile:

Reply 2

DJFearRoss

OK, so you're saying;

3x - 3 = +1x

3x - 3 = +1x - 1x
3x - 3 - 1x = 0
3x - 1x - 3 = 0
2x -3 = 0
2x -3+3 = 0+3
2x=3

2x/2 = 3/2
x = 1.5

Got it, thanks so much. I never thought about ever getting x to zero. I just assumed that would make it disappear so it couldn't be done. But of course 0 is a number, so is still valid.