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.
Correct answer is 1276.
This an arithmetic series.
Answer:
B
Step-by-step explanation:
Since the triangle is right use the tangent ratio to find x
tan64° = =
Multiply both sides by 11
x = 11 × tan64° = 22.55 → B
Answer: You will pay $510 for a item with original price of $600 when discounted 15%.
Answer:
Option A -8/3
Step-by-step explanation:
The complete question in the attached figure
we know that
Sasha started at sea level and has hiked down to the fourth rest station.
Remember that sea level is 0.
Sasha takes a break at the rest stations every 2/3 of a mile.
That means-----> Sasha is down 4 times 2/3
But the answer will be in negative as she is below 0.
therefore
Sasha’s elevation now is -8/3 miles below sea level.