Certainly! Let’s work through the steps as given in the table to find the inverse function [tex]\( f^{-1}(x) \)[/tex].
### Given
1. Step 1: Function Given
[tex]\[
f(x) = \frac{3x + 4}{8}
\][/tex]
2. Step 2: Change [tex]\( f(x) \)[/tex] to [tex]\( y \)[/tex]
[tex]\[
y = \frac{3x + 4}{8}
\][/tex]
3. Step 3: Switch [tex]\( x \)[/tex] and [tex]\( y \)[/tex]
[tex]\[
x = \frac{3y + 4}{8}
\][/tex]
### Solving for [tex]\( y \)[/tex]
4. Step 4: Multiply each side by 8 to eliminate the denominator
[tex]\[
8x = 3y + 4
\][/tex]
5. Step 5: Isolate the term containing [tex]\( y \)[/tex]
[tex]\[
8x - 4 = 3y
\][/tex]
6. Step 6: Solve for [tex]\( y \)[/tex]
[tex]\[
y = \frac{8x - 4}{3}
\][/tex]
### Conclusion
7. Step 7: Replace [tex]\( y \)[/tex] with [tex]\( f^{-1}(x) \)[/tex]
[tex]\[
f^{-1}(x) = \frac{8x - 4}{3}
\][/tex]
So, the inverse function [tex]\( f^{-1}(x) \)[/tex] is:
[tex]\[
f^{-1}(x) = \frac{8x - 4}{3}
\][/tex]
