15.3 Composition of functions (a function of a function)
WORKED EXAMPLE Explaining the idea of a function of a function
An €80 pair of shoes is on sale for 25% off the price. However, on the fi nal day of the sale the shop offers an additional 10% off the sale price. What is the price of these shoes on the fi nal day of the sale? You might think that all you have to do is to decrease €80 by 35% to get €52. This is incorrect. It is a two-stage process of two functions, g and f.
€80
First g
g takes €80 and multiplies it by 0·75: 0·75 × 80
and then
Second f
g = €60
f takes €60 and multiplies it by 0·9: 0·9 × 60
€54
Therefore, the fi nal-day price is €54. f is done after g. Mathematically, ‘f after g’ acting on x is written as ( f o g)(x) or f ( g (x)). |
