+0  
 
+1
33
3
avatar+1729 

Help.

NotSoSmart  Feb 12, 2018
Sort: 

3+0 Answers

 #1
avatar+6365 
+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
 #2
avatar+1729 
+1

can you help for 10?

NotSoSmart  Feb 12, 2018
 #3
avatar+6365 
+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 .

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

hectictar  Feb 12, 2018

8 Online Users

avatar
We use cookies to personalise content and ads, to provide social media features and to analyse our traffic. We also share information about your use of our site with our social media, advertising and analytics partners.  See details