# Simple 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?

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Homework Helper
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?

Natasha1
Homework Helper
Gold Member
2022 Award
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
Natasha1
Spot on haruspex, thank you to you both!

Natasha1
Thank you! How did you do that?

Natasha1
That's great, well done!