# Introduction to Functions

```PARIJATHA MATH
FUNCTIONS
FUNCTIONS
WHAT IS A FUNCTION?
▸ A function can be thought of as a &quot;machine&quot; that provides exactly one output for each
valid input.
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FUNCTIONS
MAIN PARTS OF A FUNCTION
▸ Input
▸ Relationship
▸ Output
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FUNCTIONS
EXAMPLES
▸ “Multiply by 6”
▸ 1&times;6=6
▸ 2 &times; 6 = 12
▸ 3 &times; 6 = 18
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FUNCTIONS
NOTATION
▸ f(x) = 6x
▸ f → function name
▸ x → input
▸ 6x → what to output
▸ Other notation f : x → 3x − 5
▸ Sometimes functions have no names y = x
2
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FUNCTIONS
QUESTIONS
▸ For f(x) = 3x − 5 evaluate
i)
f(2)
2x + 6
For f : x →
evaluate
▸
3
f(3)
f(2) = 3 &times; 2 − 5
i)
=6−5=1
ii) f(1.5)
ii) f(0)
f(0) = 3 &times; 0 − 5
=−5
iii) f(−2)
iii) f(−1)
2
For
f(x)
=
x
+ 4 evaluate
▸
i)
f(2)
f(−2) = 3 &times; (−2) − 5
ii) f(6)
= − 6 − 5 = − 11
iii) f(−1)
FUNCTIONS
INVERSE FUNCTION
▸ The inverse of a function is its reverse, i.e. it undoes the function’s effect
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FUNCTIONS
NOTATION
▸ The inverse of a function f(x) is written as f
−1
(x)
▸ Example:
▸ f(x) = 6x
x
−1
f
(x)
=
▸
6
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FUNCTIONS
QUESTIONS
Find the inverse of the following functions
(i) f(x) = x + 2
f −1(x) = x − 2
ii) g(x) = 2x − 3
x+3
g (x) =
2
−1
x−3
For f(x) =
evaluate
3
i)
−1
f (2)
ii) f
−1
(3)
FUNCTIONS
QUESTIONS
Find the inverse of the following functions
(i)
f(x) = x + 3
(i)
f(x) = 4x
ii)
g(x) = x − 5
ii)
f(x) = 2x + 5
iii)
f(x) = x + 6
iii)
f(x) = 3x − 6
iv)
g(x) = x
iv)
x+4
f(x) =
2
v)
h(x) = 2x
vi)
x
p(x) =
3
v)
3x − 2
g(x) =
4
vi)
8x + 7
g(x) =
5
1
(i) f(x) = x + 3
2
1
ii) g(x) = x − 2
4
iii) f(x) = 4(3x − 6)
iv) g(x) = 6(x + 3)
v) h(x) = − 2(−3x + 2)
2
vi) p(x) = (4x − 5)
3
```