Why add 3 instead of dividing by 3 in composite function

[Natasha1]

Homework Statement

and

Find

,

and

2. The attempt at a solution

means work out

, then work out

for this value.

so

I do not understand why we add + 3 in line before last (2 x 16 + 3)
Should it not be divided by 3 as it is

which means 3 x g(x) = x^2

I am a little stuck on the reason why?

 

[RPinPA]

I'm not sure what they're doing with the $+3$ either but $3g(x) = x^2$ so $g(x) = x^2/3$ and $g(4) = 16/3$, not 16. And $f \circ g(4)$ would be twice the value of $g(4)$, definitely not 35.

Neither the calculation for $g(4)$ nor $f[g(4)]$ is consistent with the definitions you showed. Are you sure you have the right solution for the right question?

 

[haruspex]

I suggest a typo in the question. It should read f(x)=2x+3 g(x)=x².
It would be most unusual to define g implicitly as 3g(x)=x² instead of g(x)=x²/3.

 

[Natasha1]

Therefore BBC teachers have made a mistake on this page...

https://www.bbc.com/bitesize/guides/zqpfcj6/revision/6

 

[Natasha1]

Spot on haruspex, thank you to you both!

 

[haruspex]

Therefore BBC teachers have made a mistake on this page...

https://www.bbc.com/bitesize/guides/zqpfcj6/revision/6

I have sent the BBC feedback on it.

 

[Natasha1]

Thank you! How did you do that?

 

[haruspex]

Thank you! How did you do that?

https://ssl.bbc.co.uk/faqs/forms

 

[Natasha1]

That's great, well done!