Question

find the inverse of the function.
h(x) = x - 9
write your answer in the form ax + b. simplify any fractions.
h⁻¹(x) =
↓

Explanation:

Step1: Replace h(x) with y

We start by writing the function as \( y = x - 9 \). This is a standard first step when finding the inverse of a function, as it makes it easier to swap the variables.

Step2: Swap x and y

Next, we interchange the roles of \( x \) and \( y \) to get \( x = y - 9 \). This is based on the definition of an inverse function, where if \( y = h(x) \), then \( x = h^{-1}(y) \).

Step3: Solve for y

Now, we solve the equation \( x = y - 9 \) for \( y \). To do this, we add 9 to both sides of the equation:

$$ x + 9 = y $$

This gives us the inverse function in terms of \( x \).

Step4: Write the inverse function

We can now write the inverse function \( h^{-1}(x) \) as \( h^{-1}(x)=x + 9 \).

Answer:

\( h^{-1}(x)=x + 9 \)