If `f : R rarr R` defined by `f(x) = (2x-7)/(4)` is an invertible function, then `f^(-1)` =

Options

A. `(4x + 5)/(2)`
B. `(4x + 7)/(2)`
C. `(3x + 7)/(2)`
D. `(9x + x)/(5)`

Answer

To find the inverse of the function \( f(x) = \frac{2x - 7}{4} \), we will follow these steps:

### Step 1: Replace \( f(x) \) with \( y \)
We start by rewriting the function:
\[ y = \frac{2x - 7}{4} \]

### Step 2: Solve for \( x \) in terms of \( y \)
To find the inverse, we need to express \( x \) in terms of \( y \). First, we multiply both sides by 4 to eliminate the fraction:
\[ 4y = 2x - 7 \]

Next, we add 7 to both sides:
\[ 4y + 7 = 2x \]

Now, divide both sides by 2:
\[ x = \frac{4y + 7}{2} \]

### Step 3: Replace \( y \) with \( f^{-1}(x) \)
Now that we have \( x \) in terms of \( y \), we can express the inverse function:
\[ f^{-1}(x) = \frac{4x + 7}{2} \]

### Final Answer
Thus, the inverse function is:
\[ f^{-1}(x) = \frac{4x + 7}{2} \]

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