Find the inverse function in slope-intercept form (mx+b):

Question

f, of, x, equals, start fraction, 5, divided by, 3, end fraction, x, minus, 10
f(x)=
3
5
​
x−10

Answer 1

To find the inverse function \( f^{-1}(x) \) of the function \( f(x) = \frac{5}{3}x - 10 \), we will follow these steps:

1. First, replace \( f(x) \) with \( y \): \[ y = \frac{5}{3}x - 10 \]

2. Next, solve for \( x \) in terms of \( y \): \[ y + 10 = \frac{5}{3}x \]

   Multiply both sides by \( \frac{3}{5} \) to isolate \( x \): \[ x = \frac{3}{5}(y + 10) \]

3. Now, replace \( y \) with \( x \) to find the inverse function: \[ f^{-1}(x) = \frac{3}{5}(x + 10) \]

4. We can distribute \( \frac{3}{5} \): \[ f^{-1}(x) = \frac{3}{5}x + \frac{3}{5} \cdot 10 \] \[ f^{-1}(x) = \frac{3}{5}x + 6 \]

Thus, the inverse function in slope-intercept form is: \[ f^{-1}(x) = \frac{3}{5}x + 6 \]