If `f : R rarr R, f(x) = x^(2) - 5x + 4` and `g : R^(+) rarr R, g(x) = log x`, then the value of (gof) (2) is

Options

A. 0
B. `oo`
C. `-oo`
D. Undefined

Answer

To solve the problem step by step, we need to find the value of \((g \circ f)(2)\), which means we first need to evaluate \(f(2)\) and then use that result to evaluate \(g(f(2))\).

### Step 1: Evaluate \(f(2)\)

The function \(f\) is defined as:
\[ f(x) = x^2 - 5x + 4 \]

Now, we substitute \(x = 2\):
\[ f(2) = 2^2 - 5 \cdot 2 + 4 \]
Calculating each term:
\[ = 4 - 10 + 4 \]
Combining the results:
\[ = 4 - 10 + 4 = -2 \]

### Step 2: Evaluate \(g(f(2))\)

Next, we need to evaluate \(g(f(2))\), which is \(g(-2)\). The function \(g\) is defined as:
\[ g(x) = \log x \]
However, the domain of \(g\) is restricted to positive real numbers (\(R^+\)). Since \(-2\) is not a positive real number, \(g(-2)\) is undefined.

### Final Answer

Thus, the value of \((g \circ f)(2)\) is undefined.

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