Pregunta
If the graph of the function \( f(x) = 2x + 3 \) is reflected over the line \( y = x \), what is the equation of the resulting inverse function?
Ask by Daniels Best. in South Africa
Feb 13,2025
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The inverse function is \( y = \frac{x - 3}{2} \).
Solución
To reflect the graph of f(x) = 2x + 3 over the line y = x, we essentially swap the x and y coordinates. Start with the equation:
y = 2x + 3
Swap x and y:
x = 2y + 3
Now, solve for y:
2y = x - 3
y = (x - 3)/2
This new equation, y = (x - 3)/2, is the inverse function of f, which is the result of reflecting the original graph over the line y = x.
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To find the inverse function after reflecting over the line \( y = x \), start with the equation \( y = 2x + 3 \). Swap \( x \) and \( y \) to get \( x = 2y + 3 \). Now, solve for \( y \): 1. Subtract 3 from both sides: \( x - 3 = 2y \) 2. Divide by 2: \( y = \frac{x - 3}{2} \) Thus, the equation of the resulting inverse function is \( f^{-1}(x) = \frac{x - 3}{2} \).
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