Example 2
Find the inverse function of the following function
(a) f(x)=57x
(b) f(x)=23−x
Find the inverse function of the following function
(a) f(x)=57x
(b) f(x)=23−x
Monthly Archives: April 2020
Inverse Function Example 1
Example 1
Find the inverse function of the following function
(a) f(x) = 4 – 7x,
(b) f(x)=2x+53
Find the inverse function of the following function
(a) f(x) = 4 – 7x,
(b) f(x)=2x+53
1.4 Inverse Function
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)=5x−4 , find the inverse function.
• 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)=5x−4 , find the inverse function.
Finding a new function given a composite function (Case B : Second function is given) Example 3
Example 3 (Substitution Method)
A function f is defined by f:x↦7x .
Find the function g if gf:x↦102x+3,x≠−32 .
[Note : Second function is given, use substitution method]
A function f is defined by f:x↦7x .
Find the function g if gf:x↦102x+3,x≠−32 .
[Note : Second function is given, use substitution method]
Finding a new function given a composite function (Case B : Second function is given) Example 2
Example 2 (Substitution Method)
A function f is defined by f:x↦x−1 .
Find the function g if gf:x↦4x+2,x≠−2 .
[Note : Second function is given , use substitution y = x - 1]
A function f is defined by f:x↦x−1 .
Find the function g if gf:x↦4x+2,x≠−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
Example 1 (substitution Method)
A function f is defined by f:x↦x+2 .
Find the function g if gf:x↦x2+3x+5 .
[Note : Second function is given, use substitution y = x + 2]
A function f is defined by f:x↦x+2 .
Find the function g if gf:x↦x2+3x+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
Example 3
A function f is defined by f:x↦2x+1 .
Find the function g if fg:x↦5x−2x+5,x≠−5 .
[Note : First function is given]
Click here (check for example 5)
A function f is defined by f:x↦2x+1 .
Find the function g if fg:x↦5x−2x+5,x≠−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
Example 2
A function f is defined by f:x↦2x .
Find the function g if fg:x↦x2+1 .
[Note : the first function f is given]
Click here (check for example 5)
A function f is defined by f:x↦2x .
Find the function g if fg:x↦x2+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
Example 1
A function f is defined by f:x↦2x+5 .
Find the function g if fg:x↦3x−8 .
[Note : First function f is given]
Click here (check for example 5) to learn more about function
A function f is defined by f:x↦2x+5 .
Find the function g if fg:x↦3x−8 .
[Note : First function f is given]
Click here (check for example 5) to learn more about function
Composite Function (Comparison Method) Example 2
Example 2
Given f:x↦1−x and g:x↦px2+q . If the composite function gf is defined by gf:x↦3x2−6x+5 , find
(a) the value of p and of q,
(b) the value of g2(−1) .
Given f:x↦1−x and g:x↦px2+q . If the composite function gf is defined by gf:x↦3x2−6x+5 , find
(a) the value of p and of q,
(b) the value of g2(−1) .
