Question

what is the inverse of the function f(x) = x +3?
h(x) = (1/3)x + 3
h(x) = (1/3)x - 3
h(x) = x - 3
h(x) = x + 3

Explanation:

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

We start with the function \( f(x) = x + 3 \). Replace \( f(x) \) 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 \( y \). Subtract 3 from both sides of the equation: \( y = x - 3 \).

Step4: Replace \( y \) with \( h(x) \) (the inverse function)

We replace \( y \) with \( h(x) \) to get the inverse function. So, \( h(x) = x - 3 \).

Answer:

\( h(x) = x - 3 \) (corresponding to the option: \( h(x) = x - 3 \))