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# #9 Help. ​

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#9 Help.

Feb 20, 2018

#1
+7347
+2

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

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

$$y^3\,=\,x-2$$

$$y^3+2\,=\,x \\~\\ x\,=\,y^3+2$$

So the inverse function is...

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

.
Feb 20, 2018

#1
+7347
+2

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

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

$$y^3\,=\,x-2$$

$$y^3+2\,=\,x \\~\\ x\,=\,y^3+2$$

So the inverse function is...

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

hectictar Feb 20, 2018