Page 12 - Pra U STPM 2022 Penggal 1 - Mathematics (T)

Mathematics Term 1 STPM Chapter 1 Functions

From the above examples, we make the following conclusions:
(a) The inverse of a function is not necessarily also a function.
(b) The inverse of a given function is also a function if the given function is a one-to-one function.
(c) The inverse of a many-to-one function can be a function if we restrict the domain. 1

Example 5

Find the inverse of each of the following functions, indicating its domain.
(a) f : x ↦ 3x + 5, x  R (b) f : x ↦ 2 , x ≠ 3
x – 3
Solution: (a) f(x) = 3x + 5
–1
Let f (x) = a
∴ f(a) = x
3a + 5 = x
a = x – 5
3
x – 5
–1
Hence f (x) = , x  R
3
1
–1
or f : x ↦ (x – 5), x  R
3
(b) f(x) = 2 , x ≠ 3.
x – 3
–1
Let f (x) = b
∴ f(b) = x
2 = x
b – 3
b = 2 + 3x
x
Hence, f (x) = 2 + 3x , x ≠ 0
–1
x
2 + 3x
–1
or f : x ↦ , x ≠ 0.
x

Exercise 1.2

1.
X Y
1
a
2 b
3
c
4
d
5

(a) Show that the elements in sets X and Y define a function f from set X to set Y.
(b) Find f(1) and f(3).
(c) State the domain of f.
(d) State the range of f.
(e) Is f a one-to-one function?

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01a STPM Math T T1.indd 9 3/28/18 4:20 PM