Select the correct answer.
Find the value of [tex]g(7)[/tex] for the function below.
[tex]g(x)=\frac{7}{8} x-\frac{1}{2}[/tex]
A. [tex]\frac{53}{8}[/tex]
B. [tex]\frac{45}{8}[/tex]
C. [tex]\frac{49}{8}[/tex]
D. [tex]\frac{60}{7}[/tex]
Answer (2)
Substitute x = 7 into the function g ( x ) = 8 7 x − 2 1 .
Calculate g ( 7 ) = 8 7 ( 7 ) − 2 1 .
Simplify the expression: g ( 7 ) = 8 49 − 2 1 = 8 49 − 8 4 .
Find the final value: g ( 7 ) = 8 45 .
8 45
Explanation
Understanding the problem We are given the function g ( x ) = f r a c 7 8 x − f r a c 1 2 and asked to find the value of g ( 7 ) . This means we need to substitute x = 7 into the expression for g ( x ) and simplify.
Substitution Substitute x = 7 into the function: g ( 7 ) = 8 7 ( 7 ) − 2 1
Multiplication Now, we need to simplify the expression. First, multiply f r a c 7 8 by 7 : 8 7 × 7 = 8 7 × 7 = 8 49
Finding a common denominator Next, we have: g ( 7 ) = 8 49 − 2 1 To subtract these fractions, we need a common denominator. Since 2 × 4 = 8 , we can rewrite f r a c 1 2 as f r a c 4 8 : g ( 7 ) = 8 49 − 8 4
Subtraction Now, subtract the fractions: g ( 7 ) = 8 49 − 4 = 8 45
Final Answer Therefore, the value of g ( 7 ) is f r a c 45 8 . Comparing this to the given options, we see that option B is the correct answer.
Examples
Imagine you're baking a cake and need to adjust the recipe for a different number of servings. If the original recipe uses a function to determine the amount of flour needed based on the number of people, finding g(7) would be like calculating the flour needed for 7 servings. This kind of function evaluation is useful in many real-life scenarios where you need to scale quantities or adjust parameters based on a specific input.
To find g ( 7 ) , substitute 7 into the function, simplify the expression, and calculate to get 8 45 . The correct answer among the options is B: 8 45 .
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