Without using paper and pencil, evaluate each expression given the following functions. $ƒ (x) = x + 1$ and $g (x) = x^{2}$
$open paren f with hook positive g close paren times 2$

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Understand that the notation $(\f+\g)(2)$ means you need to find the value of the function $(\f+\g)$ at $x=2$. The function $(\f+\g)(x)$ is defined as $\f(x) + \g(x)$.

Write the expression for $(\f+\g)(x)$ by adding the two given functions: $\f(x) = x + 1$ and $\g(x) = x^2$. So, $(\f+\g)(x) = (x + 1) + x^2$.

Substitute $x = 2$ into the expression: $(\f+\g)(2) = (2 + 1) + 2^2$.

Simplify the terms inside the parentheses and the exponent: $(2 + 1) = 3$ and $2^2 = 4$.

Add the simplified values together to get the final result: $3 + 4$.

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주요 개념

질문에 올바르게 답하기 위해 반드시 이해해야 하는 핵심 개념들은 다음과 같습니다.

Function Notation and Evaluation

Function notation, such as ƒ(x), represents a rule that assigns each input x to an output. Evaluating a function at a specific value means substituting that value into the function's formula and simplifying to find the output.

Function Addition (Sum of Functions)

The sum of two functions (ƒ + g)(x) is defined as ƒ(x) + g(x). To evaluate (ƒ + g)(2), you find ƒ(2) and g(2) separately, then add the results together.

Substitution and Simplification

Substitution involves replacing the variable x with a given number in the function's expression. Simplification means performing arithmetic operations to reduce the expression to a single numerical value.

Without using paper and pencil, evaluate each expression given the following functions. ƒ(x)=x+1ƒ(x)=x+1 and g(x)=x2g(x)=x^2 (ƒ+g)(2) (ƒ+g)(2)