Find the values of the inverse of a function from its graph; examples and questions are presented along with their detailed solutions and explanations.
If f is a function whose inverse is f -1, then the relationship between f and f -1 is written as:
Use the graph of f shown below to find the following,if possible,:
a) f -1(5) , b) f -1(0) , c) f -1(- 3) , d) f -1( - 4) , e) f -1(- 5)
Question 1 - Use the graph of function g shown below to find the following if possible:
a) g -1(6) , b) g -1(0) , c) g -1(- 2) , d) g -1(4) , e) g -1(8)
Question 2 - Use the graph of function h shown below to find the following if possible:
a) h -1(1) , b) h -1(0) , c) h -1(- 1) , d) h -1(2)
.
Solution to Question 1
a) According to the the definition of the inverse function:
a = g -1(6) ⇔ 6 = g(a)
Meaning that a is the value of x such g(x) = 6.
Using the graph below for x = 2, g(x) = 6. Hence a = 2 and therefore g -1(6) = 2
.
Solution to Question 2
a) According to the the definition of the inverse function:
a = h -1(1) ⇔ 1 = h(a) ,
Meaning that a is the value of x such h(x) = 1.
According to the graph shown, h(0) = 1 and therefore h -1(1) = 0.
b) a = h -1(0) ⇔ h(a) = 0
According to the graph shown, h(π/2) = 0 and therefore h -1(0) = π/2.
c) a = h -1(-1) ⇔ h(a) = -1
According to the graph shown, h(π) = - 1 and therefore h -1(-1) = π.
d) a = h -1(2) ⇔ h(a) = 2
According to the graph shown, there is no value of x for which h(x) = 2 and therefore h -1(2) is undefined.
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