For the function f, of, x, equals, 5, x, plus, 3f(x)=5x+3, find f, to the power minus 1 , left parenthesis, x, right parenthesisf

Question

−1
(x).
Answer
Multiple Choice Answers
f, to the power minus 1 , left parenthesis, x, right parenthesis, equals, 5, x, minus, 3f
−1
(x)=5x−3
f, to the power minus 1 , left parenthesis, x, right parenthesis, equals, start fraction, left parenthesis, x, minus, 3, right parenthesis, divided by, 5, end fractionf
−1
(x)=
5
(x−3)
​

f, to the power minus 1 , left parenthesis, x, right parenthesis, equals, start fraction, left parenthesis, x, plus, 3, right parenthesis, divided by, 5, end fractionf
−1
(x)=
5
(x+3)
​

f, to the power minus 1 , left parenthesis, x, right parenthesis, equals, 5, left parenthesis, x, minus, 3, right parenthesisf
−1
(x)=5(x−3)

Answer 1

To find the inverse function \( f^{-1}(x) \) for the given function \( f(x) = 5x + 3 \), we follow these steps:

1. Replace \( f(x) \) with \( y \): \[ y = 5x + 3 \]

2. Solve for \( x \) in terms of \( y \): \[ y - 3 = 5x \] \[ x = \frac{y - 3}{5} \]

3. Now switch \( x \) and \( y \) to find the inverse: \[ f^{-1}(x) = \frac{x - 3}{5} \]

Thus, the inverse function is: \[ f^{-1}(x) = \frac{x - 3}{5} \]

So the correct answer from your multiple choice options is: \[ f^{-1}(x) = \frac{x - 3}{5} \]