An equation that defines y as a function of x is given. Find ƒ(3). y+2x²=3-x

Verified step by step guidance

Start with the given equation: $y + 2x^{2} = 3 - x$.

Isolate $y$ on one side to express it as a function of $x$: subtract \$2x^{2}$ from both sides to get $y = 3 - x - 2x^{2}$.

Rewrite the function notation as $f(x) = 3 - x - 2x^{2}$ to clearly show $y$ as a function of $x$.

To find $f(3)$, substitute $x = 3$ into the function: $f(3) = 3 - (3) - 2(3)^{2}$.

Simplify the expression step-by-step by calculating the powers and performing the arithmetic to find the value of $f(3)$.

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Key Concepts

Here are the essential concepts you must grasp in order to answer the question correctly.

Function Notation and Evaluation

Function notation, such as ƒ(x), represents a rule that assigns each input x to exactly one output y. Evaluating ƒ(3) means substituting x = 3 into the function's equation and calculating the corresponding y-value.

Solving for y in Terms of x

To find ƒ(3), the equation must be rewritten to express y explicitly as a function of x. This involves isolating y on one side of the equation, often by performing algebraic operations like addition, subtraction, or division.

Substitution Method

After expressing y as a function of x, substitution involves replacing x with the given value (here, 3) to compute the specific output. This step is essential to find the function's value at a particular input.

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