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Chapter 14: Q2. (page 574)

  1. If f:x鈫�x, find the images of -3, 6, and -6.
  2. Is f a one-to-one function? Explain.

Short Answer

Expert verified

(a) The image of -3,6and -6 are 3, 6 and 6, respectively.

(b) No, the function fx=x at -3,6 and -6 is not one-to-one function.

Step by step solution

01

a.Step 1. Given Information.

The given function is f:x=x.

02

Step 2. Calculation.

To find the image for the given values of x, substitute the values of x.

Consider x=-3.

f鈭�3=鈭�3=3

Similarly,

Consider x=6.

f6=6=6

And,

Consider x=-6.

f鈭�6=鈭�6=6

03

Step 3. Conclusion.

Therefore, the image of -3,6and -6 are 3, 6 and 6, respectively.

04

b.Step 1. Given Information.

Consider the given function fx=x.

05

Step 2. Calculation.

In part (a), the image of -3,6 and -6 are 3,6 and 6, respectively. Since 6 and -6 both has image as 6. So, this is not one-to one function.

06

Step 3. Conclusion.

Therefore, the function fx=x at -3,6 and -6 is not one-to-one function.

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