Questions: Fill in the blanks. (f/g)(x) = , provided that (f/g)(x) = provided that - f(x)/g(x) - f(x)-g(x) - g(x)/f(x) - f(x) · g(x)

Solution Steps

To fill in the blanks, we need to understand the expression \(\left(\frac{f}{g}\right)(x)\). This represents the division of two functions, \(f(x)\) and \(g(x)\). The expression is defined as long as the denominator \(g(x)\) is not equal to zero. Therefore, the first blank should be filled with \(\frac{f(x)}{g(x)}\) and the condition for the second blank is \(g(x) \neq 0\).

We have two functions defined as follows:

• \( f(x) = x^2 \)
• \( g(x) = x - 1 \)

We need to evaluate both functions at \( x = 2 \):

• \( f(2) = 2^2 = 4 \)
• \( g(2) = 2 - 1 = 1 \)

Now, we calculate the division of the two functions: \[ \left(\frac{f}{g}\right)(2) = \frac{f(2)}{g(2)} = \frac{4}{1} = 4 \]

Final Answer