Answer:
21
Step-by-step explanation:
Answer:
a) and d) are bijections. b) and c) are not
Step-by-step explanation:
a) Every linear non constant function is a bijection. We can easily find the inverse of f by making a simple calculus.
If y is on the function image, we have y = -3x + 4 for certain x, then
y- 4 = -3x
-(y-4)/3 = x
therefore ![f^{-1}(x) = -(x-4)/3](https://tex.z-dn.net/?f=f%5E%7B-1%7D%28x%29%20%3D%20-%28x-4%29%2F3%20)
b) -3 * X² + 4 is not a bijection because quadratic funtions arent bijective. If you evaluate in opposite values you will obtain the same result. For example f(-1) = f(1) = 6
c) (x+1)/(x+2) is not a bijection. It isnt even defined in -2 because the denominator is equal to 0 if X= -2 and we cant divide by 0. A bijective function from R to R must be defined in every element of R. In general, homographic non linear functions are not bijective for the same reason this function is not.
d)
is bijective. There isnt a simple argument we can use to conclude this. We have no other choice than trying to find the inverse function by making a calculus.
Y = ![X^5+1](https://tex.z-dn.net/?f=%20X%5E5%2B1%20)
Y-1 = ![X^5](https://tex.z-dn.net/?f=%20X%5E5)
![(Y-1)^{1/5} = X](https://tex.z-dn.net/?f=%20%28Y-1%29%5E%7B1%2F5%7D%20%3D%20X%20)
Not that since 5 is odd, we can calculate
independently of which value Y-1 takes. Therefore
, and we can conclude that f is bijective.
I hope this helps you!
Answer:
122.6 m
Step-by-step explanation:
Shadow cast by the man = 3.1 m
Height of the man = 1.9 m
Shadow cast by the lighthouse = 200 m
Height of the lighthouse = x
If two shapes are similar, the ratio of their corresponding sides would be equal.
Therefore,
x/1.9 = 200/3.1
Multiply both sides by 1.9
x = (200*1.9)/3.1
x = 122.6 m (nearest tenth)
The lighthouse is 122.6 m tall
When we bring 6y from right side to left side it’s sign get changed and 8y-6y=2y.
36, because 60 time .4 is 24 so 60 - 24 is 36 so it is 36 dollars.
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