Let's find the inverse function \( f^{-1}(x) \) step-by-step for \( f(x) = 4x + 7 \).
1. Start with the original function:
[tex]\[ y = 4x + 7 \][/tex]
2. Swap \( x \) and \( y \):
[tex]\[ x = 4y + 7 \][/tex]
3. Solve for \( y \):
[tex]\[ x - 7 = 4y \][/tex]
4. Isolate \( y \):
[tex]\[ y = \frac{x - 7}{4} \][/tex]
5. Write the inverse function:
[tex]\[ f^{-1}(x) = \frac{x - 7}{4} \][/tex]
Arrange the steps correctly:
1. \( y = 4 x + 7 \)
2. \( x = 4 y + 7 \)
3. \( x - 7 = 4 y \)
4. \( \frac{x-7}{4}=y \)
5. \( f^{-1}(x)=\frac{x-7}{4} \)
So, the correct order of the steps is:
1. \( y = 4 x+7 \)
2. \( x = 4 y + 7 \)
3. \( x - 7 = 4 y \)
4. \( \frac{x-7}{4}=y \)
5. [tex]\( f^{-1}(x)=\frac{x-7}{4} \)[/tex]
