Question

If the function f(x) is defined as \(f(x) = 3(x + 2) + 5\), then \(f(a - 2) =\)

• A. \(3a\)
• B. \(3a + 5\)
• C. \(3a + 11\)
• D. \(3a - 1\)
• E. \(3a - 6\)

Hint:

When evaluating a function, be very careful with the substitution. It's often helpful to place parentheses around the expression you are substituting in, especially if it's more complex than a single variable. This helps avoid errors in order of operations.

Answer 1

The Correct Option is B

Step 1: Understanding the Concept:
This question tests the understanding of function notation and evaluation. To find \(f(a-2)\), we need to substitute the expression \((a-2)\) for every occurrence of \(x\) in the definition of the function \(f(x)\).
Step 2: Key Formula or Approach:
The given function is \(f(x) = 3(x + 2) + 5\).
The process involves direct substitution and algebraic simplification.
Step 3: Detailed Explanation:
We are asked to find the value of \(f(a - 2)\).
Start with the function definition: \[ f(x) = 3(x + 2) + 5 \] Substitute \(x\) with \((a - 2)\): \[ f(a - 2) = 3((a - 2) + 2) + 5 \] Now, simplify the expression inside the parentheses: \[ (a - 2) + 2 = a \] Substitute this back into the equation: \[ f(a - 2) = 3(a) + 5 \] \[ f(a - 2) = 3a + 5 \] Step 4: Final Answer:
After substituting \((a-2)\) into the function and simplifying, we find that \(f(a-2) = 3a + 5\). This corresponds to option (B).