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.
D you have to substitute the h with 27
Hope this helps
I'm pretty sure the answer is A because you're multiplying each number by 105 and A is the only answer with 105
Answer: OPTION D.
Step-by-step explanation:
The rate of change of a linear function is also known as "Slope".
The slope can be calculated with the following formula:
Choose two points on the function "R" graphed:
You can say that:
Substituting values into the formula, you get:
Choose two point from the table that models the function "S":
You can say that:
Substituting values into the formula, you get:
Therefore, you can conclude that the function "S" has a greater rate of change than Function "R".
