If `f: R to R ` is defined as f(x)=2x+5 and it is invertible , then `f^(-1) (x)` is

Options

A. `(x-5)/(2)`
B. `(x-2)/(5)`
C. `(x+5)/(2)`
D. none of these

Answer

To find the inverse of the function \( f(x) = 2x + 5 \), we will follow these steps:

### Step 1: Replace \( f(x) \) with \( y \)
We start by letting \( y = f(x) \):
\[ y = 2x + 5 \]

### Step 2: Solve for \( x \) in terms of \( y \)
Next, we need to express \( x \) in terms of \( y \). We can do this by rearranging the equation:
\[ y - 5 = 2x \]
Now, divide both sides by 2:
\[ x = \frac{y - 5}{2} \]

### Step 3: Replace \( y \) with \( x \)
To find the inverse function, we replace \( y \) with \( x \):
\[ f^{-1}(x) = \frac{x - 5}{2} \]

### Final Answer
Thus, the inverse function is:
\[ f^{-1}(x) = \frac{x - 5}{2} \]

---