Find the inverse function of the function f, of, x, equals, start fraction, 4, x, divided by, 5, end fractionf(x)=
5
4x
.
Answer
Attempt 1 out of 2
Multiple Choice Answers
f, to the power minus 1 , left parenthesis, x, right parenthesis, equals, minus, start fraction, 5, x, divided by, 4, end fractionf
−1
(x)=−
4
5x
f, to the power minus 1 , left parenthesis, x, right parenthesis, equals, start fraction, 4, x, divided by, 5, end fractionf
−1
(x)=
5
4x
f, to the power minus 1 , left parenthesis, x, right parenthesis, equals, start fraction, 5, x, divided by, 4, end fractionf
−1
(x)=
4
5x
f, to the power minus 1 , left parenthesis, x, right parenthesis, equals, minus, start fraction, 4, x, divided by, 5, end fractionf
−1
(x)=−
5
4x
1 answer
To find the inverse function of \( f(x) = \frac{4}{5}x \), we will follow these steps:
Set \( f(x) \) equal to \( y \):
\[
y = \frac{4}{5}x
\]
Swap \( x \) and \( y \):
\[
x = \frac{4}{5}y
\]
Solve for \( y \):
To isolate \( y \), first multiply both sides by \( \frac{5}{4} \):
\[
y = \frac{5}{4}x
\]
Write the inverse function:
Thus, the inverse function \( f^{-1}(x) \) is:
\[
f^{-1}(x) = \frac{5}{4}x
\]
Now let's analyze the multiple-choice options:
\( f^{-1}(x) = -\frac{5}{4}x \)
\( f^{-1}(x) = \frac{4}{5}x \)
\( f^{-1}(x) = \frac{5}{4}x \)
\( f^{-1}(x) = -\frac{4}{5}x \)
The correct inverse function is:
\[
f^{-1}(x) = \frac{5}{4}x
\]
So, the answer is:
\( f^{-1}(x) = \frac{5}{4}x \).