Question

Equation 3 h(x)=10x+3/2
find the inverse of equation 3

Answer 1

To find the inverse of the function \( h(x) = \frac{10x + 3}{2} \), we will follow these steps:

1. **Replace \( h(x) \) with \( y \)**:
\[
y = \frac{10x + 3}{2}
\]

2. **Swap \( x \) and \( y \)**:
\[
x = \frac{10y + 3}{2}
\]

3. **Solve for \( y \)**:
- First, multiply both sides by 2 to eliminate the fraction:
\[
2x = 10y + 3
\]
- Next, subtract 3 from both sides:
\[
2x - 3 = 10y
\]
- Finally, divide both sides by 10:
\[
y = \frac{2x - 3}{10}
\]

4. **Write the inverse function**:
\[
h^{-1}(x) = \frac{2x - 3}{10}
\]

So, the inverse of the function \( h(x) = \frac{10x + 3}{2} \) is \( h^{-1}(x) = \frac{2x - 3}{10} \).