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Question 99656This question is from textbook
: 1. Find the inverse of the function f(x)=x^1/3+2.
2. A bacteria culture started with a count of 720 at 8:00 A.M., and after t hours is expected to grow to f(t)=720(2/3)^t. estimate the number of bacteria in the culture at 11:00A.M. the same day.
3. if f(x)=(x+1)(x-4), use interval notation to give all values of x where f(x)>0.
4. express as a polynominal: (x+a)(x^2-ax/x).
This question is from textbook
Answer by stanbon(75887)   (Show Source):
You can put this solution on YOUR website! 1. Find the inverse of the function f(x)=x^(1/3)+2.
y = x^(1/3) + 2
Interchange x and y and solve for "Y":
x = y^(1/3)+2
y^(1/3) = x-2
y = (x-2)^3
That is the inverse.
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2. A bacteria culture started with a count of 720 at 8:00 A.M., and after t hours is expected to grow to f(t)=720(2/3)^t. estimate the number of bacteria in the culture at 11:00A.M. the same day.
f(t)=720(2/3)^t
From 8 to 11 is 3 hours
f(3) = 720(2/3)^3
f(3) = 720*(8/27) = 213 1/3
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3.If f(x)=(x+1)(x-4), use interval notation to give all values of x where f(x)>0.
The boundary of the inequality intervals is x=-1 and x=4
Draw a Real Number line and plot the values x--1 and x=4
That breaks the line into three intervals.
Test a value from each interval in (x+1)(x-4)>0 to find the solution interval(s).
In (-inf,-1) pick x=-2 ; -*->0 so solutions are in this interval
In (-1,4) pick x=0 ; +*-<0 so no solutions are in this interval
In (4,+inf) pick x=5; +*+>0 so solutions are in this interval
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Final Answer: (-inf,-1)U(4,+inf)
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4. express as a polynominal: (x+a)(x^2-ax/x).
=x(x^2-ax/x)+a(x^2-ax/x)
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Comment:
I can't tell if x is a denominator of "a" or if (x^2-ax).
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cheers,
Stan H.
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