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this table compares the functions f(x) and g(x) for given values of x

X: -2 -1 0 1 2

f(x: -1, 3/4 , 1, 1 3/4, 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)

1 answer

To compare the functions \( f(x) \) and \( g(x) \) for the given values of \( x \), we can list the outputs of both functions side by side:

\[ \begin{array}{|c|c|c|} \hline x & f(x) & g(x) \ \hline -2 & -1 & 3 \ -1 & \frac{3}{4} & \frac{3}{4} \ 0 & 1 & 0 \ 1 & \frac{7}{4} & \frac{3}{4} \ 2 & 3 & 3 \ \hline \end{array} \]

Next, we will check when \( g(x) \) is greater than \( f(x) \):

  1. For \( x = -2 \):

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

  2. For \( x = -1 \):

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

  3. For \( x = 0 \):

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

  4. For \( x = 1 \):

    • \( f(1) = \frac{7}{4} \)
    • \( g(1) = \frac{3}{4} \)
    • \( g(1) > f(1) \) (False)

  5. For \( x = 2 \):

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

Conclusion

The only instance where \( g(x) > f(x) \) is at \( x = -2 \). For all other values of \( x \) in the given table, \( g(x) \) is less than or equal to \( f(x) \).