Q. x=2∣y∣+5Find four points contained in the inverse. Express your values as an integer or simplified fraction.
Express y in terms of x: To find the inverse of the function, we first need to express y in terms of x. This means we need to solve the equation for y.
Isolate y term: Subtract 5 from both sides of the equation to isolate the term with y on one side.x−5=2∣y∣
Solve for ∣y∣: Now, divide both sides by 2 to solve for ∣y∣.(x−5)/2=∣y∣
Consider two cases: Since |y|\
Find points for inverse: Now we need to find four points that are contained in the inverse. We can choose arbitrary values for \(x and solve for y in both cases.Let's choose x=7, x=9, x=11, and x=13 as our x-values.
Point 1: x=7: For x=7: Case 1: y=2(7−5)=22=1 Case 2: y=−2(7−5)=−22=−1 So, the points are (7,1) and (7,−1).
Point 2: x=9: For x=9: Case 1: y=2(9−5)=24=2 Case 2: y=−2(9−5)=−24=−2 So, the points are (9,2) and (9,−2).
Point 3: x=11: For x=11: Case 1: y=2(11−5)=26=3 Case 2: y=−2(11−5)=−26=−3 So, the points are (11,3) and (11,−3).
Point 4: x=13: For x=13: Case 1: y=2(13−5)=28=4 Case 2: y=−2(13−5)=−28=−4 So, the points are (13,4) and (13,−4).