Find the inverse function of the function f, of, x, equals, minus, start fraction, 3, x, divided by, 4, end fractionf(x)=−

Question

4
3x
​
.

Answer 1

To find the inverse function of \( f(x) = -\frac{3}{4}x \), we will follow these steps:

1. Replace \( f(x) \) with \( y \): \[ y = -\frac{3}{4}x \]

2. Swap \( x \) and \( y \) to find the inverse: \[ x = -\frac{3}{4}y \]

3. Solve for \( y \):

   • First, multiply both sides by \( -\frac{4}{3} \) to isolate \( y \): \[ y = -\frac{4}{3}x \]

4. Thus, the inverse function \( f^{-1}(x) \) is: \[ f^{-1}(x) = -\frac{4}{3}x \]

So the inverse function is \( f^{-1}(x) = -\frac{4}{3}x \).