If `f:R rarr R` defined by
`f(x)=(2x-1)/(5)`
be an invertible function, write `f^(-1)(x)`.

Answer

To find the inverse of the function \( f(x) = \frac{2x - 1}{5} \), we will follow these steps:

### Step 1: Set the function equal to \( y \)
Let \( f(x) = y \). This gives us the equation:
\[ y = \frac{2x - 1}{5} \]

### Step 2: Solve for \( x \) in terms of \( y \)
To find the inverse, we need to express \( x \) in terms of \( y \). Start by multiplying both sides by 5 to eliminate the fraction:
\[ 5y = 2x - 1 \]

### Step 3: Isolate \( x \)
Next, add 1 to both sides:
\[ 5y + 1 = 2x \]
Now, divide both sides by 2:
\[ x = \frac{5y + 1}{2} \]

### Step 4: Write the inverse function
Since we have expressed \( x \) in terms of \( y \), we can write the inverse function \( f^{-1}(x) \) by replacing \( y \) with \( x \):
\[ f^{-1}(x) = \frac{5x + 1}{2} \]

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

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