Number Seven (7): Option (D): 3 is the value NOT included in the Domain of the Inverse Function: f(x) = 2/x + 3 is: 3
Number 8: The Intersection Point is ( 1, 1 ). Therefore, The Point on the Inverse Function f^-1(x) is ( 1, 1 )
Analysis:
Question Seven (7): To find the value Not Included in the Domain of the Inverse of the Function f(x) = 2/x + 3, We First need to find the range of the original function.
- Find the Vertical Asymptote:
The Vertical Asymptote occurs when the denominator of the fractions is equal to Zero (0). In this case, it is when X = 0.
- Find the Horizontal Asymptote:
The Horizontal Asymptote occurs when the limit of the function approaches infinity. In this case, as X approaches infinity, The fraction 2/x approaches Zero (0). So, The Horizontal Asymptote is Y = 3.
- Determine the range of the Original Function:
Since the function has a Horizontal Asymptote at Y = 3, The Range of the function is all Real Numbers except Y = 3.
- Find the Domain of the Inverse Function:
The Domain of the inverse Function is the Range of the Original Function, Hence, The Domain of the Inverse Function is All Real Numbers Except Three (3).
Number Seven (7): Option (D): 3 is the value NOT included in the Domain of the Inverse Function: f(x) = 2/x + 3 is: 3
- Step By Step Explanation For Question Eight (8):
Make a plan:
To find the point on the inverse function, We need to find the point where the Green Line f(x) = x^2 Intersects the dashed Line Y = X.
- 1 - Set the Two Functions Equal to Each Other:
X = X^2
- 2 - Rearrange the Equation to find the intersection Point:
X^2 - X = 0
X(X - 1 ) = 0
X = 0, or X = 1
Hence,Question Number Eight (8): The Intersection Point is ( 1, 1 ). Therefore, The Point on the Inverse Function f^-1(x) is ( 1, 1 ).
I hope this helps you!