For the function f, of, x, equals, start fraction, left parenthesis, x, plus, 2, right parenthesis, divided by, 5, end fractionf(x)=

Question

5
(x+2)
​
, find f, to the power minus 1 , left parenthesis, x, right parenthesisf
−1
(x).
Answer
Attempt 1 out of 2
Multiple Choice Answers
f, to the power minus 1 , left parenthesis, x, right parenthesis, equals, 5, x, plus, 2f
−1
(x)=5x+2
f, to the power minus 1 , left parenthesis, x, right parenthesis, equals, start fraction, x, divided by, 5, end fraction, minus, 2f
−1
(x)=
5
x
​
−2
f, to the power minus 1 , left parenthesis, x, right parenthesis, equals, 5, left parenthesis, x, minus, 2, right parenthesisf
−1
(x)=5(x−2)
f, to the power minus 1 , left parenthesis, x, right parenthesis, equals, 5, x, minus, 2f
−1
(x)=5x−2

Answer 1

To find the inverse function \( f^{-1}(x) \), we start with the original function given by:

\[ f(x) = \frac{x + 2}{5} \]

We will set \( f(x) = y \):

\[ y = \frac{x + 2}{5} \]

Next, we solve for \( x \) in terms of \( y \):

1. Multiply both sides by 5: \[ 5y = x + 2 \]

2. Subtract 2 from both sides: \[ x = 5y - 2 \]

Now we have expressed \( x \) in terms of \( y \). To find the inverse function, we swap \( x \) and \( y \):

\[ f^{-1}(x) = 5x - 2 \]

So, the answer is:

\[ f^{-1}(x) = 5x - 2 \]

Among the multiple choice answers, the correct one is:

\( f^{-1}(x) = 5x - 2 \).