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Identify the inverse of the function Show all steps. (1 point) f(x) = (2x - 7)/7

(2x + 5)/7

(7x + 5)/2

(x + 5)/2

(7x - 5)/2
I know it’s 7x+7/2 but that’s not an option

Answer 1

1. Replace \( f(x) \) with \( y \):
\[
y = \frac{2x - 7}{7}
\]

2. Swap \( x \) and \( y \):
\[
x = \frac{2y - 7}{7}
\]

3. Solve for \( y \):
- Multiply both sides by 7 to eliminate the denominator:
\[
7x = 2y - 7
\]
- Add 7 to both sides:
\[
7x + 7 = 2y
\]
- Divide by 2:
\[
y = \frac{7x + 7}{2}
\]

4. Replace \( y \) with \( f^{-1}(x) \):
\[
f^{-1}(x) = \frac{7x + 7}{2}
\]

Now that we have calculated the inverse function \( f^{-1}(x) \), we can simplify it.

Notice that \( f^{-1}(x) = \frac{7(x + 1)}{2} \).

However, if your options do not include this specific form, let's consider if any further simplification or match can be made with the options provided:

1. Since \( f^{-1}(x) = \frac{7x + 7}{2} \) is equivalent to \( \frac{7x + 5}{2} \) if you're looking only for a closest fit that still represents the transformation done by the inverse function.

None of the options you provided match our exact expression, so it appears there may be an issue with the available choices, or the function forms given in the options are not a direct match for the derived inverse.
not be correct.