If a function is translated 3 units to the right, in which direction will the inverse of the function be transformed?(1 point)

Question

Responses

The inverse of the given function will be translated 3 units to the left.
The inverse of the given function will be translated 3 units to the left.

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.

Answer 1

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

To find the inverse of this transformed function, we set \( y = f(x - 3) \) and solve for \( x \) in terms of \( y \). After switching \( x \) and \( y \), the inverse function will be of the form \( f^{-1}(x) + 3 \).

Thus, the inverse of the original function will be translated 3 units to the left.

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