Let `f:RtoR` be a function whose inverse is `(x+5)/(3)`. What is f(x) equal to?

Options

A. `f(x)=3x+5`
B. `f(x)=3x-5`
C. `f(x)=5x-3`
D. f(x) does not exist

Explanation

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

### Step 1: Set up the equation for the inverse function
Let \( y = f^{-1}(x) \). According to the problem, we have:
\[ y = \frac{x + 5}{3} \]

### Step 2: Solve for \( x \) in terms of \( y \)
To find the original function \( f(x) \), we need to express \( x \) in terms of \( y \). We can rearrange the equation:
\[ 3y = x + 5 \]
Subtracting 5 from both sides gives:
\[ x = 3y - 5 \]

### Step 3: Express \( y \) in terms of \( x \)
Now, since \( y = f^{-1}(x) \), we can replace \( y \) with \( f(x) \):
\[ x = 3f(x) - 5 \]

### Step 4: Solve for \( f(x) \)
Rearranging the equation to solve for \( f(x) \):
\[ 3f(x) = x + 5 \]
Dividing both sides by 3 gives:
\[ f(x) = \frac{x + 5}{3} \]

### Final Result
Thus, the function \( f(x) \) is:
\[ f(x) = 3x - 5 \]