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Chapter 2: Q21E (page 97)

Which of the functionsf fromR toR in Exercises 21 through 24 are invertible?21 f(x)=x2.

Short Answer

Expert verified

The functionfx=x2 from to is not invertible.

Step by step solution

01

Invertible Function

Functionfx is invertible iff is one-to-one function, that is there are no valuesx1鈮�x2 such that fx1=fx2.If we can find such valuesx1,x2 so thatx1鈮�x2 andfx1=fx2 thenfx is not invertible.

02

Finding such values such that x1≠x2 but f(x1)=f(x2)

It is easy to see thatf-1=f1 but -1鈮�1, sofx is not invertible.

Hence, the given function is not invertible.

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Most popular questions from this chapter

Consider the circular face in the accompanying figure. For each of the matrices A in Exercises 24 through 30, draw a sketch showing the effect of the linear transformation T(x)鈫�=Ax鈫�on this face.

26.[0110]

TRUE OR FALSE?

There exists a real number k such that the matrix[k-1-2-4k-3] fails to be invertible.

Consider the circular face in the accompanying figure. For each of the matrices A in Exercises 24 through 30, draw a sketch showing the effect of the linear transformation T(x)鈫�=Ax鈫�on this face.

30.[0001]

TRUE OR FALSE?

If the linear system A2x鈫�=b鈫� is consistent, then the systemrole="math" localid="1659352762883" Ax鈫�=b鈫� must be consistent as well.

Consider the circular face in the accompanying figure. For each of the matrices A in Exercises 24 through 30, draw a sketch showing the effect of the linear transformation T(x)鈫�=Ax鈫�on this face.

27.[100-1]
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