For g(x) = 1/2 |2x-5| + 8, g(4) involves simplifying an absolute value expression and combining fractions. Evaluating it step-by-step leads to the final answer: g(4) = 19/2.
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Let's find the value of g(4) for the function g(x) = 1/2 |2x-5| + 8.
We can solve this problem by following these steps:
Combine multiplied terms into a single fraction:
g(x) = 1(2x-5)/2 + 8
Multiply by 1:
g(x) = (2x-5)/2 + 8
Find a common denominator for the fractions:
g(x) = (2x-5)/2 + (2/2) * 8
Combine multiplied terms into a single fraction:
g(x) = (2x-5)/2 + (2 * 8)/2
Combine fractions with a common denominator:
g(x) = (2x-5 + 2 * 8)/2
Multiply the numbers:
g(x) = (2x-5 + 16)/2
Re-order terms so constants are on the left:
g(x) = (|2x-5| + 16)/2
Plug in x = 4:
g(4) = (|2(4)-5| + 16)/2
Evaluate the absolute value:
g(4) = (|3| + 16)/2
Simplify:
g(4) = (3 + 16)/2
Combine like terms:
g(4) = 19/2
Therefore, g(4) = 19/2.