Find a. (fog) (x) b. (go f) (x) c. (fog) (2) d. (go f) (2).
f(x) = 1/x, g(x)= 1/x

검증된 단계별 안내

Step 1: Understand the composition of functions. The notation (f ∘ g)(x) means f(g(x)), which involves substituting g(x) into f(x). Similarly, (g ∘ f)(x) means g(f(x)), which involves substituting f(x) into g(x).

Step 2: For part (a), calculate (f ∘ g)(x). Substitute g(x) = 1/x into f(x) = 1/x. This gives f(g(x)) = f(1/x). Replace x in f(x) with 1/x to get the expression for (f ∘ g)(x).

Step 3: For part (b), calculate (g ∘ f)(x). Substitute f(x) = 1/x into g(x) = 1/x. This gives g(f(x)) = g(1/x). Replace x in g(x) with 1/x to get the expression for (g ∘ f)(x).

Step 4: For part (c), evaluate (f ∘ g)(2). Use the expression for (f ∘ g)(x) derived in part (a) and substitute x = 2. Simplify the resulting expression.

Step 5: For part (d), evaluate (g ∘ f)(2). Use the expression for (g ∘ f)(x) derived in part (b) and substitute x = 2. Simplify the resulting expression.

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이 영상 해법은 위 문제에 도움이 된다고 튜터들이 추천한 것입니다.

영상 길이:

주요 개념

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

Function Composition

Function composition involves combining two functions to create a new function. If f(x) and g(x) are two functions, the composition (fog)(x) means applying g first and then f to the result, expressed as f(g(x)). This concept is essential for solving the given exercises, as it requires understanding how to manipulate and evaluate the functions in sequence.

Evaluating Functions

Evaluating functions means substituting a specific value into the function to find the output. For example, if f(x) = 1/x, evaluating f(2) involves substituting 2 for x, resulting in f(2) = 1/2. This skill is crucial for calculating the values of (fog)(2) and (go f)(2) in the exercises.

Reciprocal Functions

Reciprocal functions are functions of the form f(x) = 1/x, which are defined for all x except zero. They exhibit unique properties, such as having vertical asymptotes at x = 0 and being symmetric about the line y = x. Understanding the behavior of reciprocal functions is important for accurately performing the compositions and evaluations in the problem.

Find a. (fog) (x) b. (go f) (x) c. (fog) (2) d. (go f) (2). f(x) = 1/x, g(x)= 1/x