Can someone take me through this question

[wise atlas]

Like how u would answer it and ur thought process

<@&791435371564892232>

[gloomy wagon]

ok

we have to find the inverse

function of h^-1

3y=x-8

3y+8=x

h^-1=3x+8

multiply

(x-3)(3x+8)

fg would be (x-3)^2-9

than you solve for the equation

@wise atlas you get it?

[tame harbor]

first u get this

like @gloomy wagon said

then we do the other side

[gloomy wagon]

that part is correct

[tame harbor]

find h^-1

now u multiply by g(x)

[gloomy wagon]

you multiply (x-3)(3x+8)

[tame harbor]

yep

[gloomy wagon]

than

multiply 10(x^2-6x)

10x^2-60x=(x-3)(3x+8)

[tame harbor]

use quadratic formula to solve

[gloomy wagon]

is inequality

[tame harbor]

ye after u do that

0 is bigger so

its like a full inequality

its this part of the graph

[gloomy wagon]

3/7<x<8

[tame harbor]

ye

if it was bigger than 0 (>0)
then its x<3/7
x>8
right

[gloomy wagon]

Yes

[tame harbor]

thats a good question
free marks

[gloomy wagon]

Yh

[gray wedge]

How free marks

[tame harbor]

because its very easy

and it looks like a 5/6 marker

[gray wedge]

If you

inverse function soemthing

does it become y =

Y =

[tame harbor]

not exactly thats just a method to work it out

like if f(x) = 5x + 2

if you write y = 5x+2
then Rearrange for x
(y-2)/5 = x

now replace the y with x
u get (x-2)/5

and thats f^-1

[gray wedge]

why replace y with x

[tame harbor]

You just gotta allow it

theres some things that u just gotta allow

[gray wedge]

So y is just a temporary variable

[tame harbor]

i guess u can think of it like that

[gray wedge]

and then you bring the X from f(x) back

[gray wedge]

Do you have an example question of it that I can do

[tame harbor]

yes

[gray wedge]

Like that

[tame harbor]

almost

[gray wedge]

What did I do wrong ?

[tame harbor]

if u multiply the right hand side by 5

ur also multiplying 1 by 5

[gray wedge]

oh I forgot yes

[tame harbor]

id rather do y-1

then do 5(y-1)

[gray wedge]

Yeah

ok thank you

[tame harbor]

np

[gray wedge]

I’ll try this now

[tame harbor]

you know how inequalities

work

right

[gray wedge]

kind of

But you times the 10 over and switch it?

[tame harbor]

where u get x^3 from

[gray wedge]

The x^3 * x

from multiply f and g function

[cursive forge]

no shot a year 10 is cooking

[tame harbor]

U can't multiply themn

fg(x) = f of g(x)

do f(x-3)

[gray wedge]

I haven’t done this at school

Ohhh

[tame harbor]

any value inside f(x) is x
so like if we did f(5) then substitue x for 5

f(x-3) - substitute x for x-3

[gray wedge]

f of what is inside function g

[tame harbor]

yes

[gray wedge]

oh

[tame harbor]

g(x) is first

then u do f of that

[tame harbor]

😂 let him cook

[cursive forge]

do u sub x-3 into x^2-9 right

to do fg(x)

[tame harbor]

yes so

(x-3)^2 - 9

[cursive forge]

yh

thats kinda ez question

if i had that in my p2

id be happy

[tame harbor]

thats x^2 - 6x

same

[cursive forge]

its just hella long tho

[tame harbor]

the right side is correct

[tame harbor]

but for 5/6 marks willing to do that

😂

[cursive forge]

its aqa

?

[tame harbor]

edexcel

but

[cursive forge]

they have 6 marks?

wt

[tame harbor]

edexcel has had some 6 markere

aqa prolly as well

[tame harbor]

its from a predicted paper

i think thats ur old one

[gray wedge]

Wrong one

[high bloom]

Tell me why I was seeing x^3

[tame harbor]

he corrected it

[high bloom]

Bouta back out the cubic formula

[gray wedge]

… a past mistake

[tame harbor]

rearrange to make it <0

[gray wedge]

Wait I am meant to switch the sign right

[tame harbor]

replace < with = and solve using quadratic formula

[gray wedge]

quadratic formula ???

[tame harbor]

u cant factorise that

[gray wedge]

how did this function question becomes quadratic but ok

[tame harbor]

😂

[high bloom]

I would expect it

Lowkey I am never using quadratic if I can factorise

[tame harbor]

i will on a calculator paper

its faster

especially if its a longer quadratic

[high bloom]

On a calc maybe

I would still try and factorise

[cursive forge]

props for the year 10 fro doing it tho

they boutta get 9s

[high bloom]

Fr

[tame harbor]

you get x = 3/7, x = 8

the quadratic is <0
so your looking for this part of the graph

u gotta rewrite as an inequality

<0 is a clue that its one big inequality

[gray wedge]

Why we drawing a graph

[tame harbor]

Because

if the quadratic was >0

then ur answer is x>8
x<3/7

but its smaller than 0

[gray wedge]

8<0
3/7<0 the quadratic says

wait no

[tame harbor]

thats if the quadratic is >0

[gray wedge]

That’s the roots?

[tame harbor]

yes

[gray wedge]

On x axis

[tame harbor]

think of x being like this

[gray wedge]

And then do we need the turning point

[tame harbor]

here u can see x>8
x<3/7

[gray wedge]

Why u highlighted the up points yellow

[tame harbor]

thats >0

theres 2 diff ones

<0 is the curved line

underneath

thats just a normal inequality

3/7<x<8

if the symbol was <= 0
then 3/7<=x<=8

[gray wedge]

So we just need to focus on the x axis

[tame harbor]

well u dont have to draw the graph but it helps u visualise it

[tame harbor]

ye

let say

x^2 + 2 < 0
then u want the line below x axis

if x^2 + 2 > 0 then u want those 2 points above

[gray wedge]

yes

[high bloom]

Imaginary solutions I swear tho for that one 😭

[tame harbor]

💀 idk i made it up

only an example

[gray wedge]

we we even need an inequality though

why*

[tame harbor]

because its an inequality

[cursive forge]

ye

[tame harbor]

if it said "="

[gray wedge]

x = 3/7 x = 8

[tame harbor]

then just leave it like that

[cursive forge]

thats if it said =

[tame harbor]

u cant cuz the question had < symbol

[gray wedge]

Ohhhhh

So you have to make it back to inequality form

[tame harbor]

yes

[cursive forge]

if u did what u did u will prob get 4 or 5

[high bloom]

Was the question < 0 or > 0

[tame harbor]

<0

[high bloom]

Got u

[gray wedge]

This

was the question

[tame harbor]

when u rearrange to the side with positive x^2 its <0

[gray wedge]

This is what I saw

When I opened this

Then I clicked on it and the question was there

[tame harbor]

prolly a bug

[gray wedge]

yeah

The question is above the white bit

[tame harbor]

so whats ur answer

final answer

[gray wedge]

3/7 < x < 8

[tame harbor]

yeh

[gray wedge]

How do we know if it’s < or <=

[tame harbor]

question will show it

[gray wedge]

Ok

thanks

[tame harbor]

like a line below it

[gray wedge]

I understand now

[tame harbor]

with aa

why is it

um

[gray wedge]

with aa

wait what

is this new

[tame harbor]

">" with a line below it, means bigger than or equal to

just do the same steps

but use that symbol isntead

[gray wedge]

yes

[tame harbor]

"<" with line is just smaller than or equal to

same thing

[gray wedge]

thanks

[tame harbor]

np

[gray wedge]

The question is nice marks now that I understand