+0  
 
0
36
1
avatar

How can I find the inverse of f^-1?

Guest Oct 9, 2017
Sort: 

1+0 Answers

 #1
avatar+1224 
+1

\(f(x)=\sqrt{5-x}+3\) 

 

Changing this to its inverse requires a few steps.

 

1. Change \(f(x)\) to \(y\).

 

This step is pretty simple. We are switching from function notation to y=-notation. \(f(x)=\sqrt{5-x}+3\) changes to \(y=\sqrt{5-x}+3\)

 

2. Interchange x and y

 

This step is also quite simple; replace all instances of x with y and all instance of y with x.

 

\(y=\sqrt{5-x}+3\) changes to \(x=\sqrt{5-y}+3\)

 

3. Solve for y

 

This step is the hardest. Transform the equation into the form of y=.

 

\(x=\sqrt{5-y}+3\) Subtract 3 on both sides.
\(x-3=\sqrt{5-y}\) Square both sides to eliminate the square root.
\((x-3)^2=\left(\sqrt{5-y}\right)^2\) Expand the left hand side knowing that \((a-b)^2=a^2-2ab+b^2\).
\(x^2-6x+9=5-y\) Subtract 5 from both sides.
\(-y=x^2-6x+4\) Divide by -1.
\(y=-x^2+6x-4\)  
   

 

4. Consider Whether the Inverse is actually a Function

 

In this case, it is a function, so we are OK.

TheXSquaredFactor  Oct 9, 2017

32 Online Users

avatar
avatar
avatar
avatar
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