Defining of Composite functions & examples

Calculating of composite functions
Definition of composite functions

1. COMPOSITE FUNCTIONS KAZIBA STEPHEN

2. LEARNING OUTCOME By the end of this lesson, you should be able to describe and understand a composite function

3. ACTIVITY Mrs. Viola is a parent at a certain school, and she has to pay UGX 500,000 in fees. However, the school offers a 15% discount for parents who pay before January. Mrs. Viola is set to pay, and being a loyal parent to the school, the principal has offered her an additional 5% discount on the amount she will pay. Can you help Mrs. Viola calculate the final fees she is supposed to pay to the school?

4. Composite functions A composite function is a combination of two functions. You apply one function to the result of another.

5. ACTIVITY Given that f (x) = 6x + 5 and g(x) = 2x −7,find (a) fg (x) (b) fg (2)

6. Given that f (x) = x + 3 and g(x) = 6 −2X,find (a) fg (x) (b) gf (x) (c ) Comment on fg (x) and gf (x)

7. ACTIVITY

8. ACTIVITY Mrs. Viola is a parent at a certain school, and she has to pay UGX 500,000 in fees. However, the school offers a 15% discount for parents who pay before January. Mrs. Viola is set to pay, and being a loyal parent to the school, the principal has offered her an additional 5% discount on the amount she will pay. Can you help Mrs. Viola calculate the final fees she is supposed to pay to the school?

9. ACTIVITY Mrs. Viola is a parent at a certain school, and she has to pay UGX 500,000 in fees. However, the school offers a 15% discount for parents who pay before January. Mrs. Viola is set to pay, and being a loyal parent to the school, the principal has offered her an additional 5% discount on the amount she will pay. Can you help Mrs. Viola calculate the final fees she is supposed to pay to the school?

10. Activity Ronald is buying a shirt in a shop priced at UGX 100,000. The shirt is on sale at a 15% discount, and VAT in Uganda is 18%. Use composite functions to find the final amount Ronald has to pay for the shirt after the discount and VAT are applied.

11. Activity Sarah is shopping for a pair of shoes that originally costs UGX 150,000. The shop offers a 20% discount on all items, and a 12% service fee is added to the discounted price. Use composite functions to find the final price Sarah has to pay for the shoes after the discount and service fee are applied .