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# help

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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

#1
+6954
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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
Sort:

#1
+6954
+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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