The intersection would be at the point (2, 2).
This is because, graphically, the plots of f(x) and its inverse are reflections of one another across the line y = x, and (2, 2) lies on this line.
Put another way, we have f(2) = 2 = f⁻¹(2), so both f(x) and f⁻¹(x) intersect when x = 2.
Put yet another (longer) way, we can find the equation for f(x): it's a line that passes through (0, 6) and (3, 0), so it has slope -6/3 = -2. Then using the point-slope formula,
y - 6 = -2 (x - 0) ⇒ y = f(x) = -2x + 6
By definition of function inverse, we have
f(f⁻¹(x)) = x
so that with the given definition of f(x), we get
f(f⁻¹(x)) = -2 f⁻¹(x) + 6 = x
-2 f⁻¹(x) = x - 6
f⁻¹(x) = -x/2 + 3
Then we solve for x such that f(x) = f⁻¹(x). We would find x = 2 as before.
I believe it is 4. I am not 100% sure
Step-by-step explanation:
hope this helps you
,..............
Answer:
72.73
Step-by-step explanation:
Answer: There will enough to paint the outside of a typical spherical water tower.
Step-by-step explanation:
1. Solve for the radius r from the formula for calculate the volume of a sphere. as following:
2. Substitute values:
3. Substitute the value of the radius into the equation fo calculate the surface area of a sphere, then you obtain that the surface area of a typical spherical water tower is:
3. If a city has 25 gallons of paint available and one gallon of paint covers 400 square feet of surface area, you must multiply 25 by 400 square feet to know if there will be enough to paint the outside of a typical spherical water tower.
As you can see, there will enough to paint the outside of a typical spherical water tower.