Find the inverse function of the function f, of, x, equals, one fifth, x, plus, 3f(x)=

Question

5
1
​
x+3

Answer 1

To find the inverse function of \( f(x) = \frac{1}{5}x + 3 \), we can follow these steps:

1. Replace \( f(x) \) with \( y \): \[ y = \frac{1}{5}x + 3 \]

2. Swap \( x \) and \( y \): \[ x = \frac{1}{5}y + 3 \]

3. Solve for \( y \):

   • First, subtract 3 from both sides: \[ x - 3 = \frac{1}{5}y \]
   • Next, multiply both sides by 5: \[ 5(x - 3) = y \]
   • Simplify: \[ y = 5x - 15 \]

4. Write the inverse function: The inverse function is: \[ f^{-1}(x) = 5x - 15 \]

Thus, the inverse function \( f^{-1}(x) \) is \( 5x - 15 \).