Question

If a function is translated 3 units to the right, in which direction will the inverse of the function be transformed?(1 point) Responses The inverse of the given function will be translated 3 units up. The inverse of the given function will be translated 3 units up. The inverse of the given function will be translated 3 units down. The inverse of the given function will be translated 3 units down. The inverse of the given function will be translated 3 units to the right. The inverse of the given function will be translated 3 units to the right. The inverse of the given function will be translated 3 units to the left.

Answer 1

If a function \( f(x) \) is translated 3 units to the right, it can be expressed as \( f(x - 3) \).

To find the inverse function, we first set \( y = f(x) \), then solve for \( x \):

1. Replace \( y \) with \( f(x) \), which gives us \( y = f(x - 3) \).
2. To find the inverse, we swap \( x \) and \( y \): \( x = f(y - 3) \).
3. Solving for \( y \), we get \( y = f^{-1}(x) + 3 \).

This shows that the inverse function will be translated 3 units to the left.

Thus, the correct response is: The inverse of the given function will be translated 3 units to the left.