1.5.2 Inverse Function Example 4 - 6 - SPM Additional Mathematics

Example 4:
(a) If f : x → x – 2, find f ^-1 (5),

(b) if f : x \to \frac{x + 9}{x - 5}, x \neq 5, find f^{- 1} (3) .

Solution:

(a)

f (x) = x– 2

Let y = f ^-1(5)

f (y) = 5

y – 2 = 5

y = 7

therefore, f ^-1(5) = 7

(b)

\begin{array}{l} f (x) = \frac{x + 9}{x - 5} \\ Let y = f^{- 1} (3) \\ f (y) = 3 \\ \frac{y + 9}{y - 5} = 3 \\ y + 9 = 3 y - 15 \\ 2 y = 24 \\ y = 12 \\ ∴ f^{- 1} (3) = 12 \end{array}

Example 5

If

g : x \mapsto \frac{m - x}{x - 3}, x \neq 3

and

g^{- 1} (5) = 14

. Find the value of m.

Correction:
m – 14 = 55
m = 55 + 14
m = 69

Example 6 (Comparison Method)
If

f : x \mapsto \frac{m x - n}{x - 2}, x \neq 2

and

f^{- 1} : x \mapsto \frac{5 - 2 x}{2 - x}, x \neq 2.

. Find the value of m and of n,