/*! This file is auto-generated */ .wp-block-button__link{color:#fff;background-color:#32373c;border-radius:9999px;box-shadow:none;text-decoration:none;padding:calc(.667em + 2px) calc(1.333em + 2px);font-size:1.125em}.wp-block-file__button{background:#32373c;color:#fff;text-decoration:none} Problem 62 If \(f(x)=8 x-9\), evaluate \(f\... [FREE SOLUTION] | 91影视

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Chapter 3: Problem 62

If \(f(x)=8 x-9\), evaluate \(f\left(\frac{3}{5}\right)\).

Short Answer

Expert verified
The evaluated value is \( \frac{-21}{5} \).

Step by step solution

01

Understand the given function

The function provided is \( f(x) = 8x - 9 \). This means for any value of \( x \), you can find the corresponding value of \( f(x) \) by substituting \( x \) into the function.
02

Substitute the given value into the function

Substitute \( x = \frac{3}{5} \) into the function \( f(x) = 8x - 9 \). This gives us \( f\left( \frac{3}{5} \right) = 8 \left( \frac{3}{5} \right) - 9 \).
03

Simplify the expression

Multiply \( 8 \) by \( \frac{3}{5} \) to get \( \frac{24}{5} \). Now the expression is \( f\left( \frac{3}{5} \right) = \frac{24}{5} - 9 \).
04

Subtract to get the final answer

Convert \( 9 \) to a fraction with a denominator of \( 5 \), which is \( \frac{45}{5} \), and subtract from \( \frac{24}{5} \). This results in \( f\left( \frac{3}{5} \right) = \frac{24}{5} - \frac{45}{5} = \frac{24 - 45}{5} = \frac{-21}{5} \).

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Key Concepts

These are the key concepts you need to understand to accurately answer the question.

Substitute Values in Functions
First, understand the concept of a function. In mathematics, a function is a rule that assigns exactly one value to each input. For instance, our function is given by the equation \( f(x) = 8x - 9 \). This means, whatever value of \( x \) you put in, it will calculate the corresponding \( f(x) \) by following this rule.

To evaluate \( f \left( \frac{3}{5} \right) \), follow these steps:
  • Identify the value to substitute. Here, you need to substitute \( x = \frac{3}{5} \) into \( f(x) \).
  • Replace every instance of \( x \) in the function with \( \frac{3}{5} \).
Thus, \( f \left( \frac{3}{5} \right) = 8 \times \frac{3}{5} - 9 \). This will set you up to find the corresponding value for the given input.
Simplify Expressions
Simplifying expressions involves combining like terms and performing arithmetic operations to get the simplest form of the expression. In our problem, you need to simplify \( 8 \times \frac{3}{5} - 9 \).

Here鈥檚 how to do that:
  • First, multiply \( 8 \) by \( \frac{3}{5} \). The rule to multiply a whole number by a fraction is straightforward: multiply the numerator by the whole number and place it over the original denominator. This gives us \( \frac{24}{5} \).
Now the expression is \( \frac{24}{5} - 9 \).

To continue, we need to handle the fraction arithmetic.
Fraction Arithmetic
Dealing with fractions can be tricky, but it's just a matter of following some basic rules. To subtract a whole number from a fraction, perform these steps:
  • Convert the whole number to a fraction. For \( 9 \), we change it to \( \frac{45}{5} \) because both numbers must have the same denominator.
  • Now, subtract the two fractions: \( \frac{24}{5} - \frac{45}{5} \).
  • Subtract the numerators while keeping the denominator the same. This gives you \( \frac{24 - 45}{5} = \frac{-21}{5} \).
Thus, \( f \left( \frac{3}{5} \right) = \frac{-21}{5} \). This is your final answer.

Remember, practicing these steps with different numbers can further solidify your understanding of evaluating functions, simplifying expressions, and performing fraction arithmetic.

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Most popular questions from this chapter

Use the slope formula to find the slope of the line that passes through the points. \((-5,-4) ;(-9,-3)\)

(a) find the \(y\)-intercept. (b) find the \(x\)-intercept. (c) use the slope formula to find the slope of the line. \(x-y=7\)

(a) find the \(y\)-intercept. (b) find the \(x\)-intercept. (c) use the slope formula to find the slope of the line. \(2 x+3 y=9\)

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