If h(x) = 4x – 3, what is an equation for h-1(x)? O A. h-1(x) = 3x + 4 O B. h-1(x) = 3x – 4 O C. h-1) = x+3 4 D. h-12 = x-3

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### Understanding Inverse Functions: Finding \( h^{-1}(x) \)

In this exercise, we are given a function \( h(x) = 4x - 3 \) and are required to find the equation for the inverse function \( h^{-1}(x) \). Below are the options provided:

#### Question:

If \( h(x) = 4x - 3 \), what is an equation for \( h^{-1}(x) \)?

#### Options:

- A. \( h^{-1}(x) = 3x + 4 \)
- B. \( h^{-1}(x) = 3x - 4 \)
- C. \( h^{-1}(x) = \frac{x + 3}{4} \)
- D. \( h^{-1}(x) = \frac{x - 3}{4} \)

### Detailed Breakdown:
To find the inverse function \( h^{-1}(x) \), follow these steps:

1. **Write the given function**:
   \( h(x) = 4x - 3 \)

2. **Replace \( h(x) \) with \( y \)**:
   \( y = 4x - 3 \)

3. **Solve for \( x \) in terms of \( y \)**:
   \[
   y = 4x - 3
   \]
   Add 3 to both sides:
   \[
   y + 3 = 4x
   \]
   Divide by 4:
   \[
   x = \frac{y + 3}{4}
   \]

4. **Replace \( y \) with \( x \)** to get the inverse function::
   \[
   h^{-1}(x) = \frac{x + 3}{4}
   \]

Hence, the correct answer is Option C:
\[
h^{-1}(x) = \frac{x + 3}{4}
\]
Transcribed Image Text:### Understanding Inverse Functions: Finding \( h^{-1}(x) \) In this exercise, we are given a function \( h(x) = 4x - 3 \) and are required to find the equation for the inverse function \( h^{-1}(x) \). Below are the options provided: #### Question: If \( h(x) = 4x - 3 \), what is an equation for \( h^{-1}(x) \)? #### Options: - A. \( h^{-1}(x) = 3x + 4 \) - B. \( h^{-1}(x) = 3x - 4 \) - C. \( h^{-1}(x) = \frac{x + 3}{4} \) - D. \( h^{-1}(x) = \frac{x - 3}{4} \) ### Detailed Breakdown: To find the inverse function \( h^{-1}(x) \), follow these steps: 1. **Write the given function**: \( h(x) = 4x - 3 \) 2. **Replace \( h(x) \) with \( y \)**: \( y = 4x - 3 \) 3. **Solve for \( x \) in terms of \( y \)**: \[ y = 4x - 3 \] Add 3 to both sides: \[ y + 3 = 4x \] Divide by 4: \[ x = \frac{y + 3}{4} \] 4. **Replace \( y \) with \( x \)** to get the inverse function:: \[ h^{-1}(x) = \frac{x + 3}{4} \] Hence, the correct answer is Option C: \[ h^{-1}(x) = \frac{x + 3}{4} \]
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