Answer:
Domain : 0° < x <90°
Range: 90° < y < 180°.
Step-by-step explanation:
When we have a function:
f(x) = y
the domain is the set of the possible values of x, and the range is the set of the possible values of y.
In this case we have:
x + y = 180°
such that x < y
Let's analyze the possible values of x.
The smallest possible value of x must be larger than 0°, as we are workin with suplementary angles.
Knowing this, we can find the maximum value for y:
0° + y = 180°
y = 180° is the maximum of the range.
Then we have:
0° < x
y < 180°
To find the other extreme, we can use the other relation:
x < y.
Then, we can impose that x = y (this value will not be either in the range nor the domain)
if x = y then:
x + y = x + x = 180
2*x = 180
x = 90°
This will be the maximum of the domain and the minimum of the range.
Then we have that the domain is:
0° < x <90°
And the range is:
90° < y < 180°.
