Check whether following pairs of function are identical or not?
`f(x)=x` and `g(x)=e^(lnx)`

Explanation

To determine whether the functions \( f(x) = x \) and \( g(x) = e^{\ln x} \) are identical, we need to check their domains and ranges.

### Step 1: Find the domain of \( f(x) \)

The function \( f(x) = x \) is a linear function. The domain of a linear function is all real numbers.

**Domain of \( f \):**
\[ \text{Domain of } f = \mathbb{R} \]

### Step 2: Find the domain of \( g(x) \)

The function \( g(x) = e^{\ln x} \) involves the natural logarithm function. The logarithm function \( \ln x \) is defined only for \( x > 0 \). Therefore, the domain of \( g(x) \) is restricted to positive real numbers.

**Domain of \( g \):**
\[ \text{Domain of } g = (0, \infty) \]

### Step 3: Compare the domains

Now we compare the domains of both functions:
- Domain of \( f \): \( \mathbb{R} \) (all real numbers)
- Domain of \( g \): \( (0, \infty) \) (positive real numbers)

Since the domains are not equal, we can conclude that the functions are not identical.

### Step 4: Conclusion

Since the domains of \( f \) and \( g \) are not the same, we conclude that the functions \( f(x) \) and \( g(x) \) are not identical.

**Final Answer:**
The functions \( f(x) = x \) and \( g(x) = e^{\ln x} \) are not identical.

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