Functions

Question 0

Alternative notation aka mapping notation

f : x –> 2x + 3
Eg. 2
Eg. -10

Answer 0

f : 2 –> 7

f : -10 –> -17

Question 1

Notation
f(x) = 3x + 1 << doesnt always have to be f

A) f(2)
B) f(-3)
C) f(1/2)

Answer 1

A) f(2) = 3x + 1
          = 3 x 2 + 1
          = 7
B) f(-3) = 3x + 1
            = -9 + 1
            = -8
C) f(1/2) = 3x + 1
              = 1.5 + 1
              = 2.5

Question 2

Domain (input) and range (output)

f(x) = x + 3

Domain {1,2,3,4}

Answer 2

Range {4,5,6,7}

Question 3

Using algebra
g (x) = 2x(sq) + x
g (3y)

Answer 3

g (3y) = 2 (3y)(sq) + 3y
= 18y(sq) + 3y
Use brackets to help simplify!

Question 4

f : x –> 2x + 1

Domain : {-2,3,7,11}

Answer 4

Range : {-3,7,15,23}

Question 6

f (x) = 4x - 3

Domain: 1<= 5

Answer 6

Range: 1 <= 17

Note, range is given as an inequality

Question 7

Find coords of these inequalities
f(x) = 2x - 7
Domain: -2 <= 10

Answer 7

Range: -11 <= 13
therefore coords are:
(-2,-11)
(10,13)

Question 7

Cannot square negatives or divide by zero so we … The numbers in the domain that equal those

Answer 7

Exclude

Question 8

make the range correct:
f(x) =10 - 2x
Domain: -3 < x <= 5

Answer 8

Range: 16 < f(x) = f(x) > 0

Question 9

1/0 aka

Answer 9

Undefined

Question 10

f(x) = 1 /2x + 1

To work out the number to exclude we use trial and error or:

Answer 10

2x + 1 = 0
2x = -1
x = -1/2 <exclude

Question 11

f (x) = sqr -4

Cannot square root negatives therefore the domain is..

Answer 11

x >= 0

Means only numbers bigger than or equal to zero

Question 12

Bigger than sign

Answer 12

>

Question 13

Smaller than sign

Answer 13

<

Question 14

Symbol for inverse functions

Answer 14

F(sq -1) : x –>

Question 15

g (x) = 3x(sq) + 7

Find: g (sq -1) (x)

Answer 15

replace the function with y then make x the subject
y = 3x(sq) + 7
y - 7 = 3x(sq) 
x = (sqr)y-7/3
g (sq-1) (x) = (sqr) x-7/3

Question 16

Composite functions

f(x) = x(sq) + 1
g (x) = 1/x

Answer 16

fg(2):
f(1/2) = (1/2)(sq) + 1 = 1/4 + 1 = 1 1/4
gf(y):
g(y(sq) + 1) = 1 /y(sq) + 1

Question 17

Composite functions

f(x) = x + 4
g(x) = x(cb)
h(x) =2x

Answer 17

hgf(6):
hg(10)
h(1000)
=2000
f(sq)g = ffg (5):
ff(125)
f(129)
= 133
ghf(l):
gh(l + 4)
g(2l + 8)
(2l + 8) (cb)

Question 18

Inverse solution: factorisation

f(x) = 2 + 3x /x - 2

Answer 18

y = 2 +3x /x-2
Cross multiply
(x - 2)y = 2 + 3x
Expand bracket
xy - 2y = 2 + 3x
xy - 3x = 2 + 2y
Factorise 
x(y - 3) = 2 + 2y
x = 2 + 2y /y - 3
FINAL ANSWER
f(sq -1) (x) = 2 + 2x /x - 3

Question 19

Finding a range from a graph

Answer 19

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