g

(

x

)

=

x

–

2

yes

no

Write the inverse function in the form

a

x

+

b

.

Simplify any fractions.

g

–

1

(

x

)

=

To find the inverse function \( g^{-1}(x) \) for the given function \( g(x) = x - 2 \), follow these steps:

1. **Start with the equation**: 
   \[
   y = g(x) = x - 2
   \]
   Replace \( g(x) \) with \( y \).

2. **Solve for \( x \) in terms of \( y \)**:
   \[
   y = x - 2
   \]
   Add 2 to both sides:
   \[
   x = y + 2
   \]

3. **Replace \( y \) with \( x \)** to get the inverse function:
   \[
   g^{-1}(x) = x + 2
   \]

Thus, the inverse function is \( g^{-1}(x) = x + 2 \).

Would you like further clarification on any of the steps?

Here are 5 related questions you can explore:
1. How do you verify if a function and its inverse are correct?
2. What are the general steps to find the inverse of a linear function?
3. How does shifting a function horizontally affect its inverse?
4. Can all functions have an inverse? If not, why?
5. What is the significance of the line \( y = x \) in the context of inverse functions?

**Tip**: When finding an inverse function, you are essentially reversing the operations applied to the input.

g(x) = x - 2. Write the inverse function in the form ax + b. Simplify any fractions.

Discover how to find the inverse function of the linear equation g(x) = x - 2. This problem covers essential algebraic concepts, including how to reverse operations to determine the inverse in the form g^{-1}(x) = x + 2. Simplified and explained step-by-step, suitable for Grades 8-10.

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