Let A = {-2, -1, 0} and f(x) = 2x – 3 then the range of f is

To determine the range of the function \( f(x) = 2x - 3 \) when the input \( x \) is restricted to the set \( A = \{-2, -1, 0\} \), we need to evaluate the function at each element of the set \( A \). The range of a function is essentially the set of all possible output values it can produce based on the given inputs.

Calculating the Function Values

Let’s compute \( f(x) \) for each value in the set \( A \):

• For \( x = -2 \):

  \( f(-2) = 2(-2) - 3 = -4 - 3 = -7 \)

• For \( x = -1 \):

  \( f(-1) = 2(-1) - 3 = -2 - 3 = -5 \)

• For \( x = 0 \):

  \( f(0) = 2(0) - 3 = 0 - 3 = -3 \)

Identifying the Range

Now that we have calculated the function values, we can summarize them:

• \( f(-2) = -7 \)
• \( f(-1) = -5 \)
• \( f(0) = -3 \)

The outputs we obtained are \( -7, -5, \) and \( -3 \). Therefore, the range of the function \( f \) when \( x \) takes values from the set \( A \) is the set of these outputs.

Final Result

Thus, the range of \( f \) is given by:

• Range of \( f = \{-7, -5, -3\} \)

This means that when you input any of the values from set \( A \) into the function \( f(x) \), the outputs will only be \( -7, -5, \) or \( -3 \). Each of these values corresponds to one of the inputs from the set \( A \), clearly defining the range of the function.