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QuestionEvaluate the function f(x)=25x−52f(x)=\frac{2}{5} x-\frac{5}{2}. What is f(5)f(5)? Options: A) 12\frac{1}{2} B) 55 C) −12-\frac{1}{2} D) −52-\frac{5}{2}. Also, what does f(10)=32f(10)=\frac{3}{2} mean? A) Output is 32\frac{3}{2} for input 10 B) Output is 10 for input 32\frac{3}{2} C) Output is f(x)f(x) for input 10 D) Output is f(32)f\left(\frac{3}{2}\right) for input 10.

Studdy Solution

STEP 1

Assumptions1. The function is given by f(x)=5x−5f(x)=\frac{}{5} x-\frac{5}{} . We are asked to evaluate the function at x=5x=5
3. We are asked to interpret the function notation f(10)=3f(10)=\frac{3}{}

STEP 2

First, we need to substitute x=5x=5 into the function to find the value of f(5)f(5).
f(5)=25×5−52f(5)=\frac{2}{5} \times5-\frac{5}{2}

STEP 3

Calculate the value of f(5)f(5).
f(5)=2−52f(5)=2-\frac{5}{2}

STEP 4

To subtract the fractions, we need to find a common denominator. The common denominator of2 and 2\frac{}{2} is2.
f()=42−2f()=\frac{4}{2}-\frac{}{2}

STEP 5

Subtract the fractions.
f(5)=4−52f(5)=\frac{4-5}{2}

STEP 6

Calculate the value of f(5)f(5).
f(5)=−12f(5)=\frac{-1}{2}So, the correct function notation when x=5x=5 is f(5)=−12f(5)=-\frac{1}{2}, which corresponds to option C.

STEP 7

Now, let's interpret the function notation f(10)=32f(10)=\frac{3}{2}. This notation means that when the input is10, the output of the function is 32\frac{3}{2}.So, the statement that best describes the function notation f(10)=32f(10)=\frac{3}{2} is "The output is 32\frac{3}{2} when the input is10", which corresponds to option A.

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