Find the inverse function of the function f, of, x, equals, minus, start fraction, 6, x, divided by, 7, end fractionf(x)=−
7
6x
.
Answer
Attempt 1 out of 2
Multiple Choice Answers
f, to the power minus 1 , left parenthesis, x, right parenthesis, equals, minus, start fraction, 6, x, divided by, 7, end fractionf
−1
(x)=−
7
6x
f, to the power minus 1 , left parenthesis, x, right parenthesis, equals, minus, start fraction, 6, divided by, 7, x, end fractionf
−1
(x)=−
7x
6
f, to the power minus 1 , left parenthesis, x, right parenthesis, equals, minus, start fraction, 7, divided by, 6, x, end fractionf
−1
(x)=−
6x
7
f, to the power minus 1 , left parenthesis, x, right parenthesis, equals, minus, start fraction, 7, x, divided by, 6, end fractionf
−1
(x)=−
6
7x
1 answer
To find the inverse function of \( f(x) = -\frac{6}{7}x \), we will follow these steps:
Replace \( f(x) \) with \( y \):
\[
y = -\frac{6}{7}x
\]
Swap \( x \) and \( y \) (this is a key step in finding the inverse):
\[
x = -\frac{6}{7}y
\]
Solve for \( y \):
Multiply both sides by \(-\frac{7}{6}\) to isolate \( y \):
\[
y = -\frac{7}{6}x
\]
Write the inverse function:
\[
f^{-1}(x) = -\frac{7}{6}x
\]
Now let's match this result with the given multiple-choice answers:
\( f^{-1}(x) = -\frac{6x}{7} \)
\( f^{-1}(x) = -\frac{7}{6}x \)
\( f^{-1}(x) = -\frac{7}{6x} \)
\( f^{-1}(x) = -\frac{6}{7x} \)
The correct answer is:
\[
f^{-1}(x) = -\frac{7}{6}x
\]
