Answer:
"f(x)
domain: all real numbers, range: all real numbers
f–1(x)
domain: all real numbers, range: all real numbers"
Step-by-step explanation:
We can use the fact that the domain of a function and the range of its inverse are equal.
Also, the range of the function and the domain of its inverse are equal as well.
<em>Looking at the function f(x/ = -x + 5, we see that this is a line with a negative slope of 1 and a y-intercept of +5. </em>
As we know from the graph of lines, there is no restricting values in x and y. So for the original function, domain is the set of all real numbers and the range is the set of all real numbers.
For the inverse, the range is set of all real numbers and domain is also the set of all real numbers.
First answer choice is right.
Answer:
The equation would be y = x - 1
Step-by-step explanation:
In order to find the equation of the line, we first can express the two sets of data as an ordered pair. The two ordered pairs would be (3, 2) and (9, 8). Now that we have these, we can use the slope formula to find the slope.
m (slope) = (y2 - y1)/(x2 - x1)
m = (8 - 2)/(9 - 3)
m = 6/6
m = 1
Now that we have the slope, we can use either point and point slope form to get the equation.
y - y1 = m(x - x1)
y - 2 = 1(x - 3)
y - 2 = x - 3
y = x - 1
The ladder will reach 122 ft up the building.
The 120 feet of the extended ladder, since it will be leaning against the building, will be the hypotenuse of the right triangle. x will be the height from the top of the fire truck to the point where the ladder hits the building. 75° is the angle the ladder will make with the fire truck.
We have an angle, the side opposite the angle, and the hypotenuse. Opposite/hypotenuse is the ratio for sine, so we set up our equation as such:
x/120 = sin 75
Multiply both sides by 120:
120(x/120) = 120*sin 75
x = 120*sin 75
x ≈116
However, this is just from the top of the fire truck to the point where the ladder hits the building. We still add the 6 feet from the top of the truck to the ground. 116+6 = 122.
Answer:
Option C.
Step-by-step explanation:
Let
r-----> the length of each piece
we know that
To find the length of each piece, divide the total length of the rope (22 ft) by the number of pieces (8 pieces)
so
-----> equation that represent the situation
-----> the length of each piece
