Evaluate The Following Function For $b(7$\]:$b(x) = \frac{5x - 5}{3x - 16}$
Introduction
In mathematics, evaluating a function at a specific value of the variable is a crucial concept. It involves substituting the given value into the function and simplifying the expression to obtain the result. In this article, we will evaluate the function b(x) = \frac{5x - 5}{3x - 16} at x = 7.
Understanding the Function
The given function is b(x) = \frac{5x - 5}{3x - 16}. This is a rational function, which means it is the ratio of two polynomials. The numerator is 5x - 5, and the denominator is 3x - 16.
Evaluating the Function at x = 7
To evaluate the function at x = 7, we need to substitute x = 7 into the function and simplify the expression.
Step 1: Substitute x = 7 into the Function
We will replace x with 7 in the function b(x) = \frac{5x - 5}{3x - 16}.
b(7) = \frac{5(7) - 5}{3(7) - 16}
Step 2: Simplify the Expression
Now, we will simplify the expression by evaluating the expressions inside the parentheses.
b(7) = \frac{35 - 5}{21 - 16}
Step 3: Perform the Subtraction
Next, we will perform the subtraction operations inside the numerator and denominator.
b(7) = \frac{30}{5}
Step 4: Simplify the Fraction
Finally, we will simplify the fraction by dividing the numerator by the denominator.
b(7) = 6
Conclusion
In this article, we evaluated the function b(x) = \frac{5x - 5}{3x - 16} at x = 7. We substituted x = 7 into the function, simplified the expression, and obtained the result b(7) = 6.
Final Answer
The final answer is .
Related Topics
- Evaluating functions at specific values
- Rational functions
- Simplifying expressions
Further Reading
Introduction
In our previous article, we evaluated the function b(x) = \frac{5x - 5}{3x - 16} at x = 7 and obtained the result b(7) = 6. In this article, we will answer some frequently asked questions related to evaluating the function at x = 7.
Q&A
Q1: What is the function b(x) = \frac{5x - 5}{3x - 16}?
A1: The function b(x) = \frac{5x - 5}{3x - 16} is a rational function, which means it is the ratio of two polynomials. The numerator is 5x - 5, and the denominator is 3x - 16.
Q2: How do I evaluate the function at x = 7?
A2: To evaluate the function at x = 7, you need to substitute x = 7 into the function and simplify the expression. This involves replacing x with 7 in the function, simplifying the expression, and obtaining the result.
Q3: What is the result of evaluating the function at x = 7?
A3: The result of evaluating the function at x = 7 is b(7) = 6.
Q4: Can I use a calculator to evaluate the function at x = 7?
A4: Yes, you can use a calculator to evaluate the function at x = 7. However, it is always a good idea to understand the steps involved in evaluating the function and to simplify the expression manually.
Q5: What if the denominator of the function is zero?
A5: If the denominator of the function is zero, then the function is undefined at that value of x. In this case, we cannot evaluate the function at x = 7.
Q6: Can I evaluate the function at any value of x?
A6: Yes, you can evaluate the function at any value of x, as long as the denominator is not zero.
Q7: How do I simplify the expression after substituting x = 7 into the function?
A7: To simplify the expression, you need to perform the operations inside the numerator and denominator, and then simplify the fraction.
Q8: Can I use a graphing calculator to visualize the function?
A8: Yes, you can use a graphing calculator to visualize the function. This can help you understand the behavior of the function and identify any points where the function is undefined.
Conclusion
In this article, we answered some frequently asked questions related to evaluating the function b(x) = \frac{5x - 5}{3x - 16} at x = 7. We hope this article has been helpful in understanding the steps involved in evaluating the function and in simplifying the expression.
Final Answer
The final answer is .
Related Topics
- Evaluating functions at specific values
- Rational functions
- Simplifying expressions
- Graphing calculators