Let's find the inverse of the given function [tex]\( f(x) = 4x - 12 \)[/tex].
### Step-by-Step Solution
1. Write the function in terms of [tex]\( y \)[/tex]:
[tex]\[
y = 4x - 12
\][/tex]
2. Swap [tex]\( x \)[/tex] and [tex]\( y \)[/tex]. This represents the inverse relationship:
[tex]\[
x = 4y - 12
\][/tex]
3. Solve for [tex]\( y \)[/tex]:
[tex]\[
x + 12 = 4y
\][/tex]
[tex]\[
y = \frac{x + 12}{4}
\][/tex]
4. Rewrite the expression to identify the coefficients:
[tex]\[
y = \frac{1}{4}x + 3
\][/tex]
So, the inverse function [tex]\( f^{-1}(x) \)[/tex] is:
[tex]\[
f^{-1}(x) = \frac{1}{4}x + 3
\][/tex]
Thus, the coefficients for [tex]\( f^{-1}(x) \)[/tex] are:
[tex]\[
\begin{array}{l}
f^{-1}(x) = 0.25x + 3.0
\end{array}
\][/tex]
### Summary
The inverse function [tex]\( f^{-1}(x) \)[/tex] for the given function [tex]\( f(x) = 4x - 12 \)[/tex] is:
\[
f^{-1}(x) = 0.25x + 3.0 \
