Question
1. Let \( f(x)=y=2 x-3 \) and \( f: A \rightarrow R \). if \( A=\{-1,0,3\} \), what is \( f(A) \) ? A) \( (-3,0,3) \) B) \( (-1,-3,-5) \) C) \( \{-3,0,-1\} \) D) \( \{-5,-3,3\} \) E) \( \{0,3,5\} \)
Ask by Floyd Erickson. in Turkey
Jan 29,2025
Upstudy AI Solution
Tutor-Verified Answer
Answer
\( f(A) = \{-5, -3, 3\} \), seçenek D.
Solution
Verilen fonksiyon \( f(x) = 2x - 3 \) ve \( A = \{-1, 0, 3\} \).
\( f(A) \) kümesini bulmak için her bir \( A \) elemanını \( f \) fonksiyonuna uygulayalım:
1. \( f(-1) = 2*(-1) - 3 = -2 - 3 = -5 \)
2. \( f(0) = 2*0 - 3 = 0 - 3 = -3 \)
3. \( f(3) = 2*3 - 3 = 6 - 3 = 3 \)
Bu sonuçlara göre \( f(A) = \{-5, -3, 3\} \).
Doğru seçenek:
**D) \( \{-5, -3, 3\} \)**
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Simplify this solution The Deep Dive
To find \( f(A) \), we will calculate \( f(x) \) for each element in the set \( A = \{-1, 0, 3\} \). 1. For \( x = -1 \): \[ f(-1) = 2(-1) - 3 = -2 - 3 = -5 \] 2. For \( x = 0 \): \[ f(0) = 2(0) - 3 = 0 - 3 = -3 \] 3. For \( x = 3 \): \[ f(3) = 2(3) - 3 = 6 - 3 = 3 \] Now, compiling the results, we have: \[ f(A) = \{-5, -3, 3\} \] Therefore, the answer is D) \( \{-5, -3, 3\} \).
