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x: -2, -1, 0, 1, 2. f(x): -1, 3/4, 1, 1 1/4, 3. g(x): 3, 3/4, 0, 3/4, 3

compare the functions f(x) and g(x). when is g(x) greater than f(x)
g(x) is greater than f(x) when x <

1 answer

To compare the functions \( f(x) \) and \( g(x) \) at the given values, we can analyze the pairs:

  • For \( x = -2 \):

    • \( f(-2) = -1 \)
    • \( g(-2) = 3 \)
    • \( g(-2) > f(-2) \) (True)

  • For \( x = -1 \):

    • \( f(-1) = \frac{3}{4} \)
    • \( g(-1) = \frac{3}{4} \)
    • \( g(-1) = f(-1) \) (False)

  • For \( x = 0 \):

    • \( f(0) = 1 \)
    • \( g(0) = 0 \)
    • \( g(0) < f(0) \) (False)

  • For \( x = 1 \):

    • \( f(1) = 1 \frac{1}{4} = \frac{5}{4} \)
    • \( g(1) = \frac{3}{4} \)
    • \( g(1) < f(1) \) (False)

  • For \( x = 2 \):

    • \( f(2) = 3 \)
    • \( g(2) = 3 \)
    • \( g(2) = f(2) \) (False)

From the comparison, we find that \( g(x) \) is greater than \( f(x) \) only when \( x = -2 \).

So, \( g(x) \) is greater than \( f(x) \) when \( x < -1 \).