Question

Find f(6) if f(x)=|x²+4x-127|

• A. -136
• B. -36
• C. -67
• D. 67
• E. 36

Hint:

When dealing with absolute value functions, first evaluate the entire expression inside the absolute value bars. Only after you have a single number inside do you apply the absolute value rule. If the result is negative, make it positive. If it's positive or zero, leave it as is.

Answer 1

The Correct Option is D

Step 1: Understanding the Concept:
The problem asks to evaluate a function involving an absolute value at a specific point. The absolute value of a number, denoted by \(|a|\), is its distance from zero on the number line. It is always non-negative. For any real number \(a\), if \(a \geq 0\), then \(|a| = a\), and if \(a<0\), then \(|a| = -a\).
Step 2: Detailed Explanation:
The function is given by \(f(x) = |x^2 + 4x - 127|\).
We need to find the value of \(f(6)\).
First, substitute \(x = 6\) into the expression inside the absolute value bars.
\[ f(6) = |(6)^2 + 4(6) - 127| \] Calculate the terms inside the bars.
\[ f(6) = |36 + 24 - 127| \] Perform the addition.
\[ f(6) = |60 - 127| \] Perform the subtraction.
\[ f(6) = |-67| \] Finally, take the absolute value of -67. The absolute value of a negative number is its positive counterpart.
\[ f(6) = 67 \] Step 3: Final Answer:
The value of \(f(6)\) is 67.