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Image of a Function

Tool to calculate an image of a function. The image of a value z by the function f is the value of f(x) where x=z, also written f(z).

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Image of a Function -

Tag(s) : Functions, Geometry

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Image of a Function

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Tool to calculate an image of a function. The image of a value z by the function f is the value of f(x) where x=z, also written f(z).

Answers to Questions

What is the definition of an image by a function?

\( y \) is the image of \( x \) by the function \( f \) if \( f(x) = y \).

An image \( y \) exists if \( y \) belongs to the domain of definition of ( f \).

The image \( y \) by the function \( f \) is unique.

How to calculate an image of a function?

From the definition of the function

To find the image of a value \( a \) by a function \( f(x) \) whose formula is known, is equivalent to compute \( f(x = a) = f(a) \).

Example: To calculate the image of \( 2 \) by the affine function \( f(x) = 3x + 1 \) is to compute \( 3 \times 2 + 1 = 7 \). So the image of \( 2 \) by \( f \) is \( f(2) = 7 \).

From the curve of the function

Finding the image of a value \( a \) by a function \( f \) whose curve is known, is to find the ordinate of the intersection of the curve with the abscissa line \( x = a \).

Example: Finding the image of \( 1 \) by the inverse function \( f(x) = 1/x \) is finding the intersection of the abscissa line \( x = 1 \) with the curve then go down to the corresponding ordinate: \( 1 \) so \( f(1) = 1 \).

What is the difference between image and preimage?

If a function \( f \) is such that \( f(x) = a \), the preimage of \( a \) by the function \( f \) is \( x \), and the image of \( x \) by the function \( f \) is \( a \).

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