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Answer:
1) f⁻¹(x) = 6 ± 2√(x -1)
3) y = (x +4)² -2
5) y = (x -4)³ -4
Step-by-step explanation:
In general, swap x and y, then solve for y. Quadratics, as in the first problem, do not have an inverse function: the inverse relation is double-valued, unless the domain is restricted. Here, we're just going to consider these to be "solve for ..." problems, without too much concern for domain or range.
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1) x = f(y)
x = (1/4)(y -6)² +1
4(x -1) = (y-6)² . . . . . . subtract 1, multiply by 4
±2√(x -1) = y -6 . . . . square root
y = 6 ± 2√(x -1) . . . . inverse relation
f⁻¹(x) = 6 ± 2√(x -1) . . . . in functional form
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3) x = √(y +2) -4
x +4 = √(y +2) . . . . add 4
(x +4)² = y +2 . . . . square both sides
y = (x +4)² -2 . . . . . subtract 2
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5) x = ∛(y +4) +4
x -4 = ∛(y +4) . . . . . subtract 4
(x -4)³ = y +4 . . . . . cube both sides
y = (x -4)³ -4 . . . . . . subtract 4
Answer:
I'm not sure
Step-by-step explanation:
Step-by-step explanation:
It is given that,
Initial speed of the car, u = 40 m/s
Final speed of the car, v = 25 m/s
Time taken, t = 3.5 s
(a) We need to find the magnitude and direction of the car’s acceleration as it slows down. It can be calculated using formula as :
The acceleration is in the opposite direction of motion i.e. west.
(b) Let s is the distance the car travel in the 3.5-s time period. It can be calculated using the third equation of motion as
s = 113.9 meters
Hence, this is the required solution.
Answer:
Scalene triangle
Step-by-step explanation:
A scalene triangle is a triangle with three different side lengths and angle measures. Since none of the side lengths are the same length, then none of the angle measures are the same either leading the correct answer to be scalene.
