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Consider the following function.
[tex]f(x) = 4x + 7[/tex]

Place the steps for finding [tex]f^{-1}(x)[/tex] in the correct order.
[tex]
\begin{array}{c}
f^{-1}(x) = \frac{x-7}{4} \\
x = 4y + 7 \\
\frac{x-7}{4} = y \\
y = 4x + 7 \\
y = \frac{x-7}{4} \\
y - 7 = 4x
\end{array}
[/tex]

Note: Only the relevant steps should be ordered.

Sagot :

GinnyAnswer
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]
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