What is f(-2) if f(x) = 3x² + x - 1?

Understand the Problem

The question is asking us to evaluate the function f(x) = 3x² + x - 1 at x = -2. To solve it, we will substitute -2 into the function and calculate the result.

Answer

$f(-2) = 9$

Steps to Solve

Substitution of x Value

We start by substituting $x = -2$ into the function $f(x) = 3x^2 + x - 1$.

This gives us: $$ f(-2) = 3(-2)^2 + (-2) - 1 $$

Calculating the Square

Evaluate $(-2)^2$ first: $$ (-2)^2 = 4 $$

Multiply by 3

Now substitute back and multiply by 3: $$ f(-2) = 3(4) + (-2) - 1 $$

Calculating $3(4)$ gives us: $$ 3(4) = 12 $$

Final Calculation

Now substitute this result back: $$ f(-2) = 12 - 2 - 1 $$

Now perform the arithmetic: $$ 12 - 2 = 10 $$ $$ 10 - 1 = 9 $$

Final Result

Therefore, the value of the function at $x = -2$ is: $$ f(-2) = 9 $$

The final answer is $f(-2) = 9$.

More Information

When substituting values into polynomial functions, it's essential to follow the order of operations: parentheses, exponents, multiplication and division (from left to right), and addition and subtraction (from left to right). This ensures the calculations are done accurately.

Tips

Forgetting to square the value before multiplying.
Neglecting to follow the order of operations correctly, which can lead to incorrect arithmetic results.
Misunderstanding the function notation could lead to incorrect substitutions.

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