Graph the inverse for each relation below (put your answer on the same graph).
Problem 1 :
Solution:
By observing the points from the graph of f(x),
(2, 3) (1, 0) (0, 1) (1, 0) and (2, 3)
Representing it as table,
x 2 1 0 1 2 
y 3 0 1 0 3 
Inverse function:
Let f^{1}(x) be the inverse of the given function f(x). To get the points on the graph of inverse function, we have to exchange the values of x and y.
Points to the plotted to make inverse function.
x 3 0 1 0 3 
y 2 1 0 1 2 
Points on Inverse graph :
(3, 2) (0, 1) (1, 0) (0, 1) and (3, 2)
Problem 2 :
Solution:
By observing the points from the graph of f(x),
(1, 1) (0, 0) and (1, 1)
Representing it as table,
x 1 0 1 
y 1 0 1 
Inverse function:
Let f^{1}(x) be the inverse of the given function f(x). To get the points on the graph of inverse function, we have to exchange the values of x and y.
(1, 1) (0, 0) and (1, 1)
x 1 0 1 
y 1 0 1 
Problem 3 :
Solution:
By observing the graph, we get the points
Points of f(x) :
(2, 4) (0, 3) (2, 2) (4, 1)
Points to be plotted on f^{1}(x) :
(4, 2) (3, 0) (2, 2) (1, 4)
For f(x)

For f^{1}(x)

Problem 4 :
Solution:
Points of f(x) :
By observing the points from the graph of f(x),
(0, 0) (1, 1) and (4, 2)
Representing it as table,
x 0 1 4 
y 0 1 2 
Inverse function:
Let f^{1}(x) be the inverse of the given function f(x). To get the points on the graph of inverse function, we have to exchange the values of x and y.
(0, 0) (1, 1) and (2, 4)
x 0 1 2 
y 0 2 4 
Problem 5 :
a. Use the graph of the function to complete the table for f^{1}.
b. Then use the table to sketch f^{1}.
Solution:
a.
Points of f(x) :
By observing the points from the graph of f(x),
(2, 4) (1, 2) (1, 2) and (3, 3)
Representing it as table,
x 2 1 1 3 
y 4 2 2 3 
Points to be plotted on f^{1}(x) :
b.
Problem 6 :
Use the graphs of f and g to evaluate each expression.
1. f^{1}(1)
2. (g^{1})(0)
3. (f ∘ g)(0)
4. g(f(4))
5. (f^{1} ∘ g)(0)
6. (g^{1} ∘ f)(1)
7. (f ∘ g^{1})(2)
8. (f^{1} ∘ g^{1})(2)
Solution:
f(x) :
Function f(x) :

Inverse function f^{1}(x) :

g(x):
Function g(x) :

Inverse function g^{1}(x) :

1.
f^{1}(1) = 0
2.
(g^{1})(0) = 2
3.
(f ∘ g)(0) = f(g(0))
= f(1)
= 2
4.
g(f(4)) = g(3)
= 1
5.
(f^{1} ∘ g)(0) = f^{1}(g(0))
= f^{1}(1)
= 0
6.
(g^{1} ∘ f)(1) = g^{1}(f(1))
= g^{1}(2)
= 4
7.
(f ∘ g^{1})(2) = f(g^{1}(2))
= f(1)
= 2
8.
(f^{1} ∘ g^{1})(2) = f^{1}(g^{1}(2))
= f^{1}(4)
= 6
Problem 7 :
1. If the composite functions f(g(x)) = x and g(f(x)) = x then the function g is the ________ function of f.
2. The domain of f is the ________ of f^{1} and the ________ of f^{1 }is the range of f.
3. The graphs of f and f^{1 }are reflections of each other in the line ________.
4. A function f is ________ if each value of the dependent variable corresponds to exactly one value of the independent variable.
5. A graphical test for the existence of an inverse function of is called the _______ Line Test.
Solution :
1) If f ∘ g (x) = g ∘ f(x), then f and g a re inverse to each other.
2) The domain of f is range of f^{1 }and range of f is domain of f^{1.}
3) The graphs of f and f^{1 }reflection of y = x.
4) one to one
5) The horizontal line test is used to check if the function is one to one.
Problem 8 :
Match the graph of the function with the graph of its inverse function. [The graphs of the inverse functions are labeled (a), (b), (c), and (d).]
Solution :
Question a :
Some of the point in the graph a :
(1, 0) (2, 1) (3, 4)
Points on inverse function (0, 1) (1, 2) (4, 3)
Question b :
Some of the point in the graph b :
(1, 5) (2, 4) (3, 3) (6, 0) and (0, 6)
Points on inverse function (5, 1) (4, 2) (3, 3) (0, 6) (6, 0)
Question c :
Some of the point in the graph c :
(1, 1) (1, 0) (3, 2)
Points on inverse function (1, 1) (0, 1) (2, 3)
Question d :
Some of the point in the graph d :
(1, 1) (0, 0) (1, 1)
Points on inverse function (1, 1) (0, 0) (1, 1)
Answers :
Question a ==> 11
Question b ==> 10
Question c ==> 9
Question d ==> 12
May 21, 24 08:51 PM
May 21, 24 08:51 AM
May 20, 24 10:45 PM