Inverse Function Example 6 (Comparison Method)

Posted on April 18, 2020 by user

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,

Inverse Function Example 5

Posted on April 18, 2020 by user

Example 5

If $g : x \mapsto \frac{m - x}{x - 3}, x \neq 3$ and $g^{- 1} (5) = 14$ . Find the value of m.

Inverse Function Example 3

Posted on April 18, 2020 by user

Example 3
Find the inverse function of

$f (x) = \frac{3 x + 2}{5 x + 3}$

Inverse Function Example 2

Posted on April 18, 2020 by user

Example 2
Find the inverse function of the following function
(a)

$f (x) = \frac{5}{7 x}$
(b)

$f (x) = \frac{2}{3 - x}$

Inverse Function Example 1

Posted on April 18, 2020 by user

Example 1
Find the inverse function of the following function
(a) f(x) = 4 – 7x,
(b)

$f (x) = \frac{2 x + 5}{3}$

1.4 Inverse Function

Posted on April 18, 2020 by user

Inverse Functions

1. Consider the function (f : x maps to - 2) with domain A = {1, 3, 4, 7}. Then the range of the function is B = {-1, 1, 2, 5}. The arrow diagram representing this function is shown as below.

2. If the arrows of (a) are reversed, the arrow diagram in (b) is obtained. A new function having domain B and range A is formed from the function f. This new function is called the inverse function of f and is denoted by f^-1 .

3. To Find the inverse function,

$f^{- 1} (x)$ of

$f (x)$
• Put the function equal to y.
• Rearrange to give x in term of y.
• Rewrite as

$f^{- 1} (x)$ replacing y by x.

Example: Given

$f (x) = 5 x - 4$ , find the inverse function.