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, we need to find the value of \((g \circ f)(2)\), which means we first need to evaluate \(f(2)\) and then apply the function \(g\) to that result.

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

The function \(f\) is defined as:
\[ f(x) = x^2 - 5x + 4 \]
Now, we substitute \(x = 2\) into the function:
\[ f(2) = 2^2 - 5(2) + 4 \]
Calculating this step-by-step:
- \(2^2 = 4\)
- \(-5(2) = -10\)
- So, \(f(2) = 4 - 10 + 4\)

Now, simplify:
\[ f(2) = 4 - 10 + 4 = -2 \]

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

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

### Conclusion

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