`f:R to R` is a function defined by f(x)=`10x -7, if g=f^(-1)` then g(x)=

Options

A. `(1)/(10x-7)`
B. `(1)/(10x+7)`
C. `(x+7)/(10)`
D. `(x-7)/(10)`

Explanation

To find the inverse function \( g(x) \) of the given function \( f(x) = 10x - 7 \), we will follow these steps:

### Step 1: Set up the equation
We start with the equation of the function:
\[ y = f(x) = 10x - 7 \]

### Step 2: Solve for \( x \)
We need to express \( x \) in terms of \( y \). Rearranging the equation gives:
\[ y + 7 = 10x \]
Now, divide both sides by 10:
\[ x = \frac{y + 7}{10} \]

### Step 3: Write the inverse function
Since \( g(x) \) is defined as \( f^{-1}(x) \), we can replace \( y \) with \( x \) in the equation we found:
\[ g(x) = f^{-1}(x) = \frac{x + 7}{10} \]

### Final Answer
Thus, the inverse function \( g(x) \) is:
\[ g(x) = \frac{x + 7}{10} \]

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