Short Answer

What is the image of a function f from $ℝ$ to $ℝ$ given by
$f (t) = t^{3} + a t^{2} + b t + c$ ,
where a,b,c are arbitrary scalars?

The image is (f) $= \{f (t) = t^{3} + a t^{2} + b t + c : t i n T\}$ ,image is all of $ℝ$ .

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Step by Step Solution

TABLE OF CONTENTS :

TABLE OF CONTENTS

Step 1: Consider the parameters.

The image of a function consists of all the values the function takes in its target space. If f is a function from X to Y, then

$i m a g e (f) = \{f (x) : i n X\} = \{b i n Y : b = f (x), for some x in X\}$

The Kernel of the transformation results in $\{f (t) = t^{3} + a t^{2} + b t + c : t i n T\}$ , as the reflection is its own inverse.

As the inverse of the reflection exists thus, the image will be $ℝ$ . The kernel is of dimension $i m a g e (f) = \{f (t) = t^{3} + a t^{2} + b t = c : t i n T\}$ so, the image will be of $ℝ$ .

Step 2: Final answer.

The image is $i m a g e (f) = \{f (t) = t^{3} + a t^{2} + b t + c : t i n T\}$ , image is all of $ℝ$ .

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Linear Algebra With Applications

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Short Answer

What is the image of a function f from $ℝ$ to $ℝ$ given by
$f (t) = t^{3} + a t^{2} + b t + c$ ,
where a,b,c are arbitrary scalars?

Step by Step Solution

Step 1: Consider the parameters.

Step 2: Final answer.

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Linear Algebra With Applications

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Short Answer

What is the image of a function f from ℝ to ℝ given by f(t)=t3+at2+bt+c ,where a,b,c are arbitrary scalars?

Step by Step Solution

Step 1: Consider the parameters.

Step 2: Final answer.

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What is the image of a function f from $ℝ$ to $ℝ$ given by
$f (t) = t^{3} + a t^{2} + b t + c$ ,
where a,b,c are arbitrary scalars?