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Suppose f(x)= 9/5x -4. Does f have an inverse? If so, find f^{-1}(20). If not, enter "undef".

waffles  Oct 24, 2017

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 #1
avatar+5229 
+2

f(x)  =  \(\frac95\)x - 4

                                    Instead of  " f(x) " , let's say  " y ".

y  =  \(\frac95\)x - 4

                                    Add  4  to both sides of the equation.

y + 4  =  \(\frac95\)x

                                    Multiply both sides of the equation by  \(\frac59\) .

\(\frac59\)(y + 4)  =  \(\frac59\) * \(\frac95\)x

 

\(\frac59\)y + \(\frac{20}9\)  =  x

 

x  =  \(\frac59\)y + \(\frac{20}9\)

 

Now, to get the inverse function, swap  x  and  y .

 

y  =  \(\frac59\)x + \(\frac{20}9\)          This is the inverse function.

 

f-1(x)  =  \(\frac59\)x + \(\frac{20}9\)          To find f-1(20) , plug in  20  for  x .

 

f-1(20)  =  \(\frac59\)(20) + \(\frac{20}9\)   =   \(\frac{100}9\) + \(\frac{20}9\)   =   \(\frac{120}9\)   =   \(\frac{40}3\)

hectictar  Oct 25, 2017
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1+0 Answers

 #1
avatar+5229 
+2
Best Answer

f(x)  =  \(\frac95\)x - 4

                                    Instead of  " f(x) " , let's say  " y ".

y  =  \(\frac95\)x - 4

                                    Add  4  to both sides of the equation.

y + 4  =  \(\frac95\)x

                                    Multiply both sides of the equation by  \(\frac59\) .

\(\frac59\)(y + 4)  =  \(\frac59\) * \(\frac95\)x

 

\(\frac59\)y + \(\frac{20}9\)  =  x

 

x  =  \(\frac59\)y + \(\frac{20}9\)

 

Now, to get the inverse function, swap  x  and  y .

 

y  =  \(\frac59\)x + \(\frac{20}9\)          This is the inverse function.

 

f-1(x)  =  \(\frac59\)x + \(\frac{20}9\)          To find f-1(20) , plug in  20  for  x .

 

f-1(20)  =  \(\frac59\)(20) + \(\frac{20}9\)   =   \(\frac{100}9\) + \(\frac{20}9\)   =   \(\frac{120}9\)   =   \(\frac{40}3\)

hectictar  Oct 25, 2017

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