Let f(x) = x² − x + 4 and g(x) = 3x – 5. Find g (1) and f(g(1)).

검증된 단계별 안내

First, identify the given functions: \(f(x) = x^{2} - x + 4\) and \(g(x) = 3x - 5\).

Calculate \(g(1)\) by substituting \(x = 1\) into the function \(g(x)\): \(g(1) = 3(1) - 5\).

Simplify the expression for \(g(1)\) to find its value.

Next, find \(f(g(1))\) by substituting the value of \(g(1)\) into the function \(f(x)\): \(f(g(1)) = (g(1))^{2} - g(1) + 4\).

Simplify the expression for \(f(g(1))\) by squaring \(g(1)\), subtracting \(g(1)\), and then adding 4 to get the final expression.

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주요 개념

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

Function Evaluation

Function evaluation involves substituting a specific input value into the function's formula to find the corresponding output. For example, to find g(1), replace x with 1 in g(x) = 3x - 5 and simplify.

Composite Functions

A composite function like f(g(1)) means applying one function to the result of another. First, evaluate the inner function g(1), then use that output as the input for the outer function f.

Polynomial and Linear Functions

Understanding the types of functions involved helps in evaluation. Here, f(x) is a quadratic polynomial (degree 2), and g(x) is a linear function (degree 1), which affects how you substitute and simplify expressions.