Question

find the inverse for f^-1(x)=x/20-3/20

Answer 1

To find the inverse of the function given in the form \( f^{-1}(x) = \frac{x}{20} - \frac{3}{20} \), we can follow these steps:

1. **Set \( y \) equal to \( f^{-1}(x) \)**:
\[
y = \frac{x}{20} - \frac{3}{20}
\]

2. **Solve for \( x \) in terms of \( y \)**:
\[
y + \frac{3}{20} = \frac{x}{20}
\]
Multiply both sides by 20:
\[
20y + 3 = x
\]

3. **Express \( f(y) \) and swap \( x \) and \( y \)**:
This gives us the original function:
\[
f(y) = 20y + 3
\]
We want to express this as \( f^{-1}(x) \):
\[
f(x) = 20x + 3
\]

4. **Interchange \( x \) and \( y \)**:
To find the inverse, we write:
\[
y = 20x + 3
\]
Hence, the inverse function is
\[
f^{-1}(x) = \frac{x - 3}{20}
\]

So the inverse function \( f(x) \) of \( f^{-1}(x) = \frac{x}{20} - \frac{3}{20} \) is:

\[
f(x) = 20x + 3
\]

Thus, the inverse function is:

\[
f^{-1}(x) = \frac{x - 3}{20}
\]