Question

show the steps to find the inverse function:
y = -2x + 7
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Explanation:

Step1: Swap x and y

To find the inverse of a function \( y = f(x) \), we first swap the roles of \( x \) and \( y \). So for the function \( y = -2x + 7 \), we get:
\( x = -2y + 7 \)

Step2: Solve for y

Now we need to isolate \( y \) on one side of the equation. First, we subtract 7 from both sides:
\( x - 7 = -2y \)
Then, we divide both sides by -2 to solve for \( y \):
\( y=\frac{-(x - 7)}{2}=\frac{-x + 7}{2}=-\frac{1}{2}x+\frac{7}{2}\)

Answer:

The inverse function of \( y = -2x + 7 \) is \( y = -\frac{1}{2}x+\frac{7}{2} \)