How to determine if a function graph has an inverse and if the inverse is a function

👉 Learn how to find the inverse of a function. The inverse of a function is a function that reverses the "effect" of the original function. One important property of the inverse of a function is that when the inverse of a function is made the argument (input) of a function, the result is x.

Given the graph of a function, we will want to determine first whether the given graph is the graph of a function, this we can achieve using the vertical line test. If a vertical line drawn at any point on the graph intersects the graph at exactly one point, then the graph is the graph of a function.

Next, we check if the given graph has an inverse, this we can achieve using the horizontal line test. If a horizontal line drawn at any point on the graph intersects the graph at exactly one point, then the graph has an inverse. To find the inverse of the function, we reflect the graph of the function across the line y = x.

Organized Videos:
✅ Find the Inverse of a Function
✅ Find the Inverse of a Function | Linear
✅ Find the Inverse of a Function | Rational
✅ Find the Inverse of a Function | Cubic
✅ Find the Inverse of a Function | Quadratic
✅ Find the Inverse of a Function | Cube Root
✅ Find the Inverse of a Function | Square Root
✅ Find the Inverse of a Function | Table
✅ Find the Inverse of a Function | Graph
✅ How to Prove Two Functions are Inverses

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[TheHonchoofAllSpearheads]

6:13 because as mentioned previously, the horizontal line intersects the original function's graph at two points, hence the function is many-to-one relation = No Inverse Fn.

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[blisterycrane]

i watching this now, cause i just stuffed my functions test.

[bpmgbvb]

hi.y=x^2 is not one to one
you can finde inverse or not

[jennyke]

Please help the following:

Find the inverse of f(x)=1-|2ln(x-1)|, restrict if necessary. 
There is no inverse function for this one since there are 2 roots if f(x)=0
Is it right? Please help. 

How to do with piecewise function?