To find \( f(x) = g(x) - h(x) \), we first need to calculate \( g(x) \) and \( h(x) \).
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Calculate \( g(x) \): \[ g(x) = 4^2 - 2 = 16 - 2 = 14 \] Since \( g(x) \) is a constant value of 14 for all \( x \).
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Calculate \( h(x) \): \[ h(x) = x^2 - 3x + 1 \]
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Substituting \( g(x) \) and \( h(x) \) into the equation: \[ f(x) = g(x) - h(x) = 14 - (x^2 - 3x + 1) \]
Now, simplifying this: \[ f(x) = 14 - x^2 + 3x - 1 \] \[ f(x) = -x^2 + 3x + 13 \]
Now, let’s look for the options provided:
a) \( 5x^2 + 4 \)
b) \( -5x^2 + 6 \)
c) \( -5x^2 + 6x + 6 \)
d) \( 5x^2 + 6x + 4 \)
None of the provided options match \( f(x) = -x^2 + 3x + 13 \). It seems like the function might have been calculated incorrectly, or the options don't correctly represent the functions involved here.
The value derived for \( f(x) \) stands at: \[ f(x) = -x^2 + 3x + 13 \]
Hence, based on the function relationship and calculations shown above, none of the options clearly represents the computed \( f(x) \).
If you were looking for \( f(x) \) in a different context or wanted any changes to the definition, please clarify for further assistance!