Question

Find the inverse function of the function f, of, x, equals, minus, start fraction, 3, x, divided by, 4, end fractionf(x)=−
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 \( f^{-1}(x) = -\frac{4}{3}x \).