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Answer
Para encontrar \( F^{-1}(3) \), usamos a função inversa \( F^{-1}(y) = \frac{y + 3}{2} \) e substituímos \( y \) por 3. Assim, \( F^{-1}(3) = 3 \).
Solution
Para encontrar \( F^{-1}(3) \), primeiro precisamos determinar a função inversa \( F^{-1}(x) \) da função \( F(x) = 2x - 3 \).
1. Começamos substituindo \( F(x) \) por \( y \):
\[
y = 2x - 3
\]
2. Agora, isolamos \( x \) em termos de \( y \):
\[
y + 3 = 2x
\]
\[
x = \frac{y + 3}{2}
\]
3. Assim, a função inversa é:
\[
F^{-1}(y) = \frac{y + 3}{2}
\]
Agora, para encontrar \( F^{-1}(3) \):
\[
F^{-1}(3) = \frac{3 + 3}{2} = \frac{6}{2} = 3
\]
Portanto, \( F^{-1}(3) = 3 \).
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Simplify this solution The Deep Dive
To find \( F^{-1}(3) \), we first set \( F(x) \) equal to 3. So, we need to solve the equation \( 2x - 3 = 3 \). Adding 3 to both sides gives \( 2x = 6 \), then dividing by 2 results in \( x = 3 \). Therefore, \( F^{-1}(3) = 3 \). Remember, the process of finding an inverse function often involves setting the original function equal to \( y \), swapping \( x \) and \( y \), and then solving for \( y \). It's a fun little dance of equations! Just make sure you’re comfortable with algebra to avoid common mix-ups!
