What is the inverse of the function \(f(x) = 3x - 5\)?

What is the inverse of the function \(f(x) = 3x - 5\)?

• A. f^{-1}(x) = \frac{x + 5}{3}
• B. f^{-1}(x) = 3x + 5
• C. f^{-1}(x) = \frac{x - 5}{3}
• D. f^{-1}(x) = 5 - 3x

Answer: (A)

To find the inverse of the function \(f(x) = 3x - 5\), we need to follow specific steps. The goal is to express \(x\) in terms of \(y\) when we set \(y = f(x)\). 1. Start with the function: \[ y = 3x - 5 \] 2. Next, solve for \(x\) in terms of \(y\): - First, add 5 to both sides: \[ y + 5 = 3x \] - Then, divide both sides by 3: \[ x = \frac{y + 5}{3} \] 3. Now, replace \(y\) with \(x\) in the expression to denote the inverse function: \[ f^{-1}(x) = \frac{x + 5}{3} \] This result shows that the inverse of \(f(x) = 3x - 5\) is indeed \(f^{-1}(x) = \frac{x + 5}{3}\). When looking at the other options, they do not satisfy

To find the inverse of the function (f(x) = 3x - 5), we need to follow specific steps. The goal is to express (x) in terms of (y) when we set (y = f(x)).

1. Start with the function:

[

y = 3x - 5

]

2. Next, solve for (x) in terms of (y):

• First, add 5 to both sides:

[

y + 5 = 3x

]

• Then, divide both sides by 3:

[

x = \frac{y + 5}{3}

]

3. Now, replace (y) with (x) in the expression to denote the inverse function:

[

f^{-1}(x) = \frac{x + 5}{3}

]

This result shows that the inverse of (f(x) = 3x - 5) is indeed (f^{-1}(x) = \frac{x + 5}{3}).

When looking at the other options, they do not satisfy