For each of the piecewise-defined functions, determine whether or not the function is one-to-one, and if it is, determine its inverse function.f(x)={(x , when x < 0),(2x, when x >=0):}

coexpennan 2021-02-24 Answered

For each of the piecewise-defined functions, determine whether or not the function is one-to-one, and if it is, determine its inverse function.
f(x)={xwhen x<02xwhen x0

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Expert Answer

avortarF
Answered 2021-02-25 Author has 113 answers

Step 1
When x is less than 0 then also y is less than zero
if x1x2forx1,x2<0
Then, y1y2
if x0 , then y is also greater than 0.
if x3x4forx3,x4<0
Then 2x32x4
So, y3y4
This means it is a one-to-one function
Step 2
To find the inverse functions we switch x and y and then solve for y
For, x<0
y=x
Or, x=y
For x0
y=2x
Or, x=2y
Or, y=x2
Result:
f1(x)={xx<0x2x0

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