Question

1. apply the horizontal or vertical line test to determine if the inverse of the function will be a function. is the inverse of the function a function?

options: yes, no

1. if ( x = 3 + 5i ) and ( y = -2 + 7i ), what is ( y - x )?

options: ( -5 + 2i ), ( 1 + 12i ), ( -1 - 12i ), ( 5 - 2i )

1. if ( x = 4 - 5i ) and ( y = -4 - 7i ), what is ( x + y )?

options: ( -2i ), ( 8 + 12i ), ( -8 ), ( -12i )

Explanation:

Step1: Check horizontal line test

Any horizontal line intersects the graph at most once, so the original function is one-to-one. Thus, its inverse is a function.

Step2: Subtract complex numbers

Substitute $x=3+5i$, $y=-2+7i$:
$y-x=(-2+7i)-(3+5i)=(-2-3)+(7i-5i)=-5+2i$

Step3: Add complex numbers

Substitute $x=4-5i$, $y=-4-7i$:
$x+y=(4-5i)+(-4-7i)=(4-4)+(-5i-7i)=-12i$

Answer:

1. Yes
2. $-5 + 2i$
3. $-12i$