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The tables represent the functions f(x) and g(x).

A table showing g(x) equals 2 x plus 15 with 2 columns and 7 rows. The first column, x, has the entries, negative 15, negative 12, negative 9, negative 6, negative 3, 0. The second column, g(x), has the entries, negative 15, blank, blank, blank, blank, 15.
Which input value produces the same output value for the two functions?

x = –12
x = –9
x = –6
x = –3

1 answer

To find the input value that produces the same output for the functions \( f(x) \) and \( g(x) \), we first need to determine the values of \( g(x) \) for the given \( x \) values in the table.

We can calculate \( g(x) \) at the provided input values using the function \( g(x) = 2x + 15 \):

  1. For \( x = -12 \): \[ g(-12) = 2(-12) + 15 = -24 + 15 = -9 \]

  2. For \( x = -9 \): \[ g(-9) = 2(-9) + 15 = -18 + 15 = -3 \]

  3. For \( x = -6 \): \[ g(-6) = 2(-6) + 15 = -12 + 15 = 3 \]

  4. For \( x = -3 \): \[ g(-3) = 2(-3) + 15 = -6 + 15 = 9 \]

Now we have calculated the outputs of \( g(x) \):

  • \( g(-12) = -9 \)
  • \( g(-9) = -3 \)
  • \( g(-6) = 3 \)
  • \( g(-3) = 9 \)

To determine which value produces the same output for \( f(x) \), we need more information about the function \( f(x) \). If you're looking for outputs from function \( f \) or if you want to compare specific outputs, please provide the values or further details about \( f(x) \) so we can make the comparison. Otherwise, we have all the outputs calculated from \( g(x) \) now.

If \( f(x) \) is not given, we cannot determine where \( f(x) = g(x) \). Please provide more context or the function \( f(x) \) to proceed!