Q. x=−4∣y∣+3Find four points contained in the inverse. Express your values as an integer or simplified fraction.
Interchanging roles of x and y: To find the inverse of the given relation, we need to solve for y in terms of x. This means we will interchange the roles of x and y and then solve for y. The original relation is x=−4∣y∣+3.
Expressing relation with interchanged variables: First, we express the relation with y and x interchanged: y=−4∣x∣+3.
Considering absolute value: Now, we need to consider the absolute value. Since |x|\
Case \(1: x is non-negative: Case 1: If x is non-negative (x≥0), then ∣x∣=x, and the equation becomes y=−4x+3.
Finding points for Case 1: From Case 1, we can find two points by choosing non-negative values for x and calculating the corresponding y values. Let's choose x=0 and x=1.
Case 2: x is negative: For x=0: y=−4(0)+3=3. So, one point is (0,3).
Finding points for Case 2: For x=1: y=−4(1)+3=−1. So, another point is (1,−1).
Finding points for Case 2: For x=1: y=−4(1)+3=−1. So, another point is (1,−1).Case 2: If x is negative (x < 0), then ∣x∣=−x, and the equation becomes y=−4(−x)+3=4x+3.
Finding points for Case 2: For x=1: y=−4(1)+3=−1. So, another point is (1,−1).Case 2: If x is negative (x < 0), then ∣x∣=−x, and the equation becomes y=−4(−x)+3=4x+3.From Case 2, we can find two more points by choosing negative values for x and calculating the corresponding y values. Let's choose x=−1 and y=−4(1)+3=−10.
Finding points for Case 2: For x=1: y=−4(1)+3=−1. So, another point is (1,−1).Case 2: If x is negative (x < 0), then ∣x∣=−x, and the equation becomes y=−4(−x)+3=4x+3.From Case 2, we can find two more points by choosing negative values for x and calculating the corresponding y values. Let's choose x=−1 and y=−4(1)+3=−10.For x=−1: y=−4(1)+3=−12. So, another point is y=−4(1)+3=−13.
Finding points for Case 2: For x=1: y=−4(1)+3=−1. So, another point is (1,−1).Case 2: If x is negative (x < 0), then ∣x∣=−x, and the equation becomes y=−4(−x)+3=4x+3.From Case 2, we can find two more points by choosing negative values for x and calculating the corresponding y values. Let's choose x=−1 and y=−4(1)+3=−10.For x=−1: y=−4(1)+3=−12. So, another point is y=−4(1)+3=−13.For y=−4(1)+3=−10: y=−4(1)+3=−15. So, the last point is y=−4(1)+3=−16.