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Nostrana [21]
3 years ago
13

If m(x)=x+5/x-1 and n(x)=x-3 which function has the same domain as (m•n)(x)

Mathematics
1 answer:
worty [1.4K]3 years ago
6 0
Consider the functions m and n:


i) m(x)=\frac{x+5}{x-1}   for x≠1.

the domain of m is  all the real numbers except 1.


ii) n(x)=x-3 is a polynomial function, because x-3 is a linear polynomial. 

The domain of any polynomial function is all real numbers. To determine the Range of this function, let c be a value in the range:

x-3=c, then x=3+c.

so if we want the function to produce c, we just set x=3+c, check:

n(3+c)=(3+c)-3=c.

This means that the Range of n is all real numbers.


What this means, is that the input (x) of the function n(x) can be any real number, and the output (n(x)) can also be any number.

so let n(x)=a, consider m(a):

m(a)=(a+5)/(a-1), clearly a≠1, this means n(x)=x-3≠1, that is x≠-4
 

This means that the domain of the composed function, m(n(x)) =  say f(x), 

is all Real numbers except 4.


Check: letting x be 4, would mean n(4)=4-3=1

which would mean m(n(4))=m(1)=(1+5)/(1-1)=6/0, which makes no sense.


Answer: Any function with domain R-{4}, has the same domain of (mon)(x) 

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0.000064 = 0.0064% probability that the box will contain less than the advertised weight of 466 g.

Step-by-step explanation:

Normal Probability Distribution:

Problems of normal distributions can be solved using the z-score formula.

In a set with mean \mu and standard deviation \sigma, the z-score of a measure X is given by:

Z = \frac{X - \mu}{\sigma}

The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the p-value, we get the probability that the value of the measure is greater than X.

N(489,6)

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What is the probability that the box will contain less than the advertised weight of 466 g?

This is the p-value of Z when X = 466. So

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0.000064 = 0.0064% probability that the box will contain less than the advertised weight of 466 g.

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