Let `g:RtoR` be a function such that, `g(x)=2x+5`. Then, what is `g^(-1)(x)` equal to ?

Options

A. `(x-5)/(2)`
B. 2x-5
C. `x-(5)/(2)`
D. `(x)/(2)+(5)/(2)`

Explanation

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

### Step 1: Set the function equal to \( y \)
Let \( y = g(x) \). Therefore, we have:
\[ y = 2x + 5 \]

### Step 2: Solve for \( x \) in terms of \( y \)
To find the inverse function, we need to express \( x \) in terms of \( y \). Start by isolating \( x \):
\[ y - 5 = 2x \]
Now, divide both sides by 2:
\[ x = \frac{y - 5}{2} \]

### Step 3: Write the inverse function
Now that we have \( x \) in terms of \( y \), we can express the inverse function \( g^{-1}(x) \) by replacing \( y \) with \( x \):
\[ g^{-1}(x) = \frac{x - 5}{2} \]

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

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