#9 Help. ​

1)

P(x)   =   55,000√[x - 1945]

 

In which year was the population 275,000  ?

 

What is the value of  x  when  P(x)  =  275,000   ?

 

275,000   =   55,000√[x - 1945]

                                                     Divide both sides by  55,000 .

5   =   √[x - 1945]

                                             Square both sides of the equation.

25   =   x - 1945

                                             Add  1945  to both sides.

1970   =   x

 

In the year  1970  , the population was  275,000 .

 

2)

\(f(x)\,=\,\sqrt[3]{x-2}\)

                                       Instead of  f(x)  let's write  y .

\(y\,=\,\sqrt[3]{x-2}\)

                                       Now let's solve this equation for  x . Raise both sides to the power of  3

\(y^3\,=\,x-2\)

                                       Add  2  to both sides.

\(y^3+2\,=\,x \\~\\ x\,=\,y^3+2\)

                                       So the inverse function is...

\(f^{-1}(x)\,=\,x^3+2\)