Chapter 17 - Algebra and Functions (Pure)

Question 1

how to do ‘proof by contradiction’ ?

Answer 1

to prove a statement by contradiction you start by saying ‘suppose the statement isn’t true’ you then show something is impossible

Question 2

how to simplify expressions?

Answer 2

look for common factors- factorise top and bottom and see if ti cancels

if there’s a fraction in the numerator or denominator, multiply the whole function by the same factor to remove it :)

Question 3

how to add or subtract two fractions?

Answer 3

before you can add or subtract the factors must have a common denominator. then add or subtract normally on top of the denominator

Question 4

how to multiply and divide algebraic fractions?

Answer 4

you multiply algebraic fraction in exactly the same way the you multiply normal fractions.

to divide by an algebraic you multiply what’s being divided by the reciprocal of the divider.

Question 5

what does the domain and range look like?

Answer 5

Question 6

what is a one-to-one function?

Answer 6

a function is one-to-one if each value in the range corresponds to only one in the domain

Question 7

when is a many-to-one function?

Answer 7

a function is many-to-one if some values in the range corresponds to more than one value in the domain

Question 8

how to find the inverse of a function?

Answer 8

to find the inverse of a function:

1) replace f(x) with y
2) rearrange to make x the subject
3) replace x with f-1(x)
4) swap round domain and range

Question 9

what is the modulus of x?

Answer 9

the modulus of x is written as /x/

Question 10

what are partial fractions?

Answer 10

you can split a fraction with more than one linear factor in the denominator ( bottom bit ) into partial fractions

Question 11

what to do with repeated factors?

Answer 11

the power shows how many times it should show up in the partial fractions.

e,g squared with have one to the power one and one to the power of two :)