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.

Finding a new function given a composite function (Case B : Second function is given) Example 3

Posted on April 18, 2020 by user

Example 3 (Substitution Method)
A function f is defined by

f : x \mapsto \frac{7}{x}

.
Find the function g if

g f : x \mapsto \frac{10}{2 x + 3}, x \neq - \frac{3}{2}

.

[Note : Second function is given, use substitution method]

Finding a new function given a composite function (Case B : Second function is given) Example 2

Posted on April 18, 2020 by user

Example 2 (Substitution Method)
A function f is defined by

f : x \mapsto x - 1

.
Find the function g if

g f : x \mapsto \frac{4}{x + 2}, x \neq - 2

.

[Note : Second function is given , use substitution y = x - 1]

Finding a new function given a composite function (Case B : Second function is given) Example 1

Posted on April 18, 2020 by user

Example 1 (substitution Method)
A function f is defined by

f : x \mapsto x + 2

.
Find the function g if

g f : x \mapsto x^{2} + 3 x + 5

.

[Note : Second function is given, use substitution y = x + 2]

Finding a new function given a composite function (Case A : First function is given) Example 3

Posted on April 18, 2020 by user

Example 3
A function f is defined by

f : x \mapsto 2 x + 1

.
Find the function g if

f g : x \mapsto \frac{5 x - 2}{x + 5}, x \neq - 5

.

[Note : First function is given]

Click here (check for example 5)

Finding a new function given a composite function (Case A : First function is given) Example 2

Posted on April 18, 2020 by user

Example 2
A function f is defined by

f : x \mapsto \frac{2}{x}

.
Find the function g if

f g : x \mapsto x^{2} + 1

.

[Note : the first function f is given]

Click here (check for example 5)

Finding a new function given a composite function (Case A : First function is given) Example 1

Posted on April 18, 2020 by user

Example 1
A function f is defined by

f : x \mapsto 2 x + 5

.
Find the function g if

f g : x \mapsto 3 x - 8

.

[Note : First function f is given]

Click here (check for example 5) to learn more about function

Composite Function (Comparison Method) Example 2

Posted on April 18, 2020 by user

Example 2
Given

f : x \mapsto 1 - x

and

g : x \mapsto p x^{2} + q

. If the composite function gf is defined by

g f : x \mapsto 3 x^{2} - 6 x + 5

, find
(a) the value of p and of q,
(b) the value of

g^{2} (- 1)

.