nagasenaz

2020-11-08

For each of the piecewise-defined functions in determine whether or not the function is one-to-one, and if it is, determine its inverse function.

yunitsiL

Skilled2020-11-09Added 108 answers

Step 1

Let

Then we get,

Let us consider two numbers

Also let us assume,

(x + y)(x - y) = 0

(x + y) = 0, (x - y) = 0

x = -y, x = y

Therefore for two elements x and -x we have

Hence f is not one-to-one for

Step 2

Let

Then we get,

f(x) = x

Let us assume for two elements x and y both greater than or equal to zero, their images are same.

So we get,

f(x) = f(y)

x = y

So for

Hence f is one-to-one function.

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?

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