Question

write an equation of the inverse for the one-to-one function as defined.\\( b(x) = x - 3 \\)\
the equation of the inverse is \\( b^{-1}(x) = \square \\).

Explanation:

Step1: Replace \( b(x) \) with \( y \)

We start with the function \( b(x) = x - 3 \). Replace \( b(x) \) with \( y \), so we have \( y = x - 3 \).

Step2: Swap \( x \) and \( y \)

To find the inverse, we swap the roles of \( x \) and \( y \). This gives us \( x = y - 3 \).

Step3: Solve for \( y \)

Now we solve the equation \( x = y - 3 \) for \( y \). Add 3 to both sides of the equation: \( x + 3 = y \).

Step4: Replace \( y \) with \( b^{-1}(x) \)

Finally, we replace \( y \) with \( b^{-1}(x) \) to get the inverse function. So \( b^{-1}(x) = x + 3 \).

Answer:

\( x + 3 \)