Question:
What is the value of the function f(x) = 6x² + 16x - 6 when x = -3?
What is the value of the function f(x) = 6x² + 16x - 6 when x = -3?
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When substituting negative numbers, always use parentheses to avoid calculation errors. For example, writing \(-3^2\) is ambiguous and often interpreted as \(-(3^2) = -9\), whereas the correct evaluation requires \((-3)^2 = 9\). Using parentheses clarifies the operation and helps prevent common mistakes.
Updated On: Oct 3, 2025
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The Correct Option is C
Solution and Explanation
Step 1: Understanding the Concept:
To evaluate a function at a specific value, we substitute that value for the variable (\(x\)) everywhere it appears in the function's expression. Then, we simplify the expression using the standard order of operations (PEMDAS/BODMAS).
Step 2: Detailed Explanation:
The function is given by \(f(x) = 6x^2 + 16x - 6\).
We need to find the value of \(f(-3)\).
Substitute \(x = -3\) into the expression:
\[ f(-3) = 6(-3)^2 + 16(-3) - 6 \] First, calculate the exponent. Remember that squaring a negative number results in a positive number.
\[ (-3)^2 = 9 \] Substitute this back into the equation:
\[ f(-3) = 6(9) + 16(-3) - 6 \] Next, perform the multiplications.
\[ 6(9) = 54 \] \[ 16(-3) = -48 \] Substitute these values back:
\[ f(-3) = 54 - 48 - 6 \] Finally, perform the subtraction from left to right.
\[ f(-3) = (54 - 48) - 6 \] \[ f(-3) = 6 - 6 \] \[ f(-3) = 0 \] Step 3: Final Answer:
The value of the function when \(x = -3\) is 0.
To evaluate a function at a specific value, we substitute that value for the variable (\(x\)) everywhere it appears in the function's expression. Then, we simplify the expression using the standard order of operations (PEMDAS/BODMAS).
Step 2: Detailed Explanation:
The function is given by \(f(x) = 6x^2 + 16x - 6\).
We need to find the value of \(f(-3)\).
Substitute \(x = -3\) into the expression:
\[ f(-3) = 6(-3)^2 + 16(-3) - 6 \] First, calculate the exponent. Remember that squaring a negative number results in a positive number.
\[ (-3)^2 = 9 \] Substitute this back into the equation:
\[ f(-3) = 6(9) + 16(-3) - 6 \] Next, perform the multiplications.
\[ 6(9) = 54 \] \[ 16(-3) = -48 \] Substitute these values back:
\[ f(-3) = 54 - 48 - 6 \] Finally, perform the subtraction from left to right.
\[ f(-3) = (54 - 48) - 6 \] \[ f(-3) = 6 - 6 \] \[ f(-3) = 0 \] Step 3: Final Answer:
The value of the function when \(x = -3\) is 0.
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