Function f is defined by equation: 2 1.) What is f(2)? 2.) What is f(3)? HELP PLS
1 answer:
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Consider the functions m and n:
i)
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)
i)
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)
Answer:
hours.
Step-by-step explanation:
We have been given that a chemical spill is leaking into a river flowing 2 3/4 miles per hour.
To find the time taken by chemical to reach the town we will divide distance of town from the spill by distance covered by chemical spill in one hour.
Upon converting our mixed fractions into improper fractions we will get,
Dividing a fraction with another fraction is same as multiplying first fraction by the reciprocal of second fraction.
After cancelling out 4 we will get,
Therefore, it will take the chemicals hours to reach the town.