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Help. ​

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Help. Feb 12, 2018

#1
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9.

P(x)   =   55000√[ x - 1945 ]

In which year was the population of the city  220,000 ? That is, what is  x  when  P(x) = 220,000 ?

220,000   =   55000√[ x - 1945 ]

Divide both sides of the equation by  55000

4   =   √[ x - 1945 ]

Square both sides of the equation.

16   =   x - 1945

Add  1945  to both sides.

1961   =   x

Check:    P(1961)   =   55000√[ 1961 - 1945 ]   =   55000√[ 16 ]   =   55000(4)   =   220,000

Feb 12, 2018
#2
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can you help for 10?

NotSoSmart  Feb 12, 2018
#3
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10.

f(x)  =  $$\sqrt{x-4}$$

Instead of  f(x)  write  y .

y   =   $$\sqrt{x-4}$$

Raise both sides to the power of  3 .

y3   =   x - 4

Add  4  to both sides.

y3 + 4  =   x

Now we have solved the original function for  x , so the inverse function is...

f-1(x)   =   x3 + 4

If  f(x)  and  f-1(x)  are inverses, then on a graph they should be a reflection of each other about the line y = x .  Here's a graph to check that:  https://www.desmos.com/calculator/oeidolt8op

Feb 12, 2018