To find the inverse of the function [tex]\( f(x) = 4x + 7 \)[/tex], let's go through the steps methodically.
1. Start with the given function and replace [tex]\( f(x) \)[/tex] with [tex]\( y \)[/tex]:
[tex]\[
y = 4x + 7
\][/tex]
2. Swap the variables [tex]\( x \)[/tex] and [tex]\( y \)[/tex] to solve for [tex]\( y \)[/tex]:
[tex]\[
x = 4y + 7
\][/tex]
3. Isolate [tex]\( y \)[/tex] on one side of the equation:
[tex]\[
x - 7 = 4y
\][/tex]
4. Solve for [tex]\( y \)[/tex] by dividing both sides by 4:
[tex]\[
y = \frac{x - 7}{4}
\][/tex]
5. The inverse function [tex]\( f^{-1}(x) \)[/tex] is:
[tex]\[
f^{-1}(x) = \frac{x - 7}{4}
\][/tex]
Following these steps, the correct order of steps can be matched with the given tiles:
- [tex]\( x = 4y + 7 \)[/tex]
- [tex]\( x - 7 = 4y \)[/tex]
- [tex]\( \frac{x - 7}{4} = y \)[/tex]
- [tex]\( f^{-1}(x) = \frac{x-7}{4} \)[/tex]
Thus, the sequence is:
[tex]\[ x=4y+7 \rightarrow x-7=4y \rightarrow \frac{x-7}{4}=y \rightarrow f^{-1}(x)=\frac{x-7}{4} \][/tex]
