For which nonnegative value of b is the expression `(1)/(2-b^(2))` undefined?

Options

A. 0
B. `sqrt2`
C. 2
D. 8

Answer

To determine the nonnegative value of \( b \) for which the expression \( \frac{1}{2 - b^2} \) is undefined, we need to follow these steps:

### Step 1: Identify when the expression is undefined
The expression \( \frac{1}{2 - b^2} \) is undefined when the denominator equals zero. Therefore, we set the denominator equal to zero:

\[ 2 - b^2 = 0 \]

### Step 2: Solve for \( b^2 \)
Rearranging the equation gives us:

\[ b^2 = 2 \]

### Step 3: Take the square root of both sides
To find \( b \), we take the square root of both sides:

\[ b = \sqrt{2} \quad \text{or} \quad b = -\sqrt{2} \]

### Step 4: Consider nonnegative values
Since we are looking for nonnegative values of \( b \), we discard \( -\sqrt{2} \) because it is negative. Thus, we have:

\[ b = \sqrt{2} \]

### Conclusion
The nonnegative value of \( b \) for which the expression \( \frac{1}{2 - b^2} \) is undefined is:

\[ \boxed{\sqrt{2}} \]

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