Topic/Skill Definition/Tips Example
Topic: Functions
1. Function Takes an input value, performs some
Machine operations and produces an output value.
2. Function A relationship between two sets of values. f ( x )=3 x 2−5
‘For any input value, square the term, then
multiply by 3, then subtract 5’.
3. Function f (x) f ( x )=3 x +11
notation x is the input value Suppose the input value is x=5
f (x) is the output value. The output value is f ( 5 )=3 ×5+11=26
4. Inverse −1
f (x)
5
f ( x )=(1−2 x) . Find the inverse.
function A function that performs the opposite
5
process of the original function. y=(1−2 x)
√ y=1−2 x
5
1. Write the function as y=f (x ) 1− √5 y=2 x
2. Rearrange to make x the subject.
1−√ y
5
3. Replace the y with x and the x with =x
2
f −1 ( x )
( x )= √
5
−1 1− x
f
2
5. Composite A combination of two or more functions 1
f ( x )=5 x−3 , g ( x )= x+1
function to create a new function. 2
fg( x) is the composite function that What is fg ( 4 ) ?
substitutes the function g ( x ) into the 1
g ( 4 )= × 4+1=3
function f ( x ) . 2
f ( 3 )=5 ×3−3=12=fg ( 4 )
fg( x) means ‘do g first, then f’
gf (x) means ‘do f first, then g’ What is fg( x)?
Subject: Maths fg ( x )=5 ( 12 x +1)−3= 52 x+2
Mr A. Coleman Glyn School
Topic: Functions
1. Function Takes an input value, performs some
Machine operations and produces an output value.
2. Function A relationship between two sets of values. f ( x )=3 x 2−5
‘For any input value, square the term, then
multiply by 3, then subtract 5’.
3. Function f (x) f ( x )=3 x +11
notation x is the input value Suppose the input value is x=5
f (x) is the output value. The output value is f ( 5 )=3 ×5+11=26
4. Inverse −1
f (x)
5
f ( x )=(1−2 x) . Find the inverse.
function A function that performs the opposite
5
process of the original function. y=(1−2 x)
√ y=1−2 x
5
1. Write the function as y=f (x ) 1− √5 y=2 x
2. Rearrange to make x the subject.
1−√ y
5
3. Replace the y with x and the x with =x
2
f −1 ( x )
( x )= √
5
−1 1− x
f
2
5. Composite A combination of two or more functions 1
f ( x )=5 x−3 , g ( x )= x+1
function to create a new function. 2
fg( x) is the composite function that What is fg ( 4 ) ?
substitutes the function g ( x ) into the 1
g ( 4 )= × 4+1=3
function f ( x ) . 2
f ( 3 )=5 ×3−3=12=fg ( 4 )
fg( x) means ‘do g first, then f’
gf (x) means ‘do f first, then g’ What is fg( x)?
Subject: Maths fg ( x )=5 ( 12 x +1)−3= 52 x+2
Mr A. Coleman Glyn School
