#1**+2 **

**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

hectictar Feb 12, 2018

#3**+2 **

**10.**

f(x) = \(\sqrt[3]{x-4}\)

Instead of f(x) write y .

y = \(\sqrt[3]{x-4}\)

Raise both sides to the power of 3 .

y^{3} = x - 4

Add 4 to both sides.

y^{3} + 4 = x

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

f^{-1}(x) = x^{3} + 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

hectictar Feb 12, 2018