Questions: Given that f(x)=x^2-6 and g(x)=3x+4, find (f-g)(-2), if it exists. Select the correct choice below and, if necessary, fill in the answer box to complete your choice. A. (f-g)(-2)= (Simplify your answer.) B. The value for (f-g)(-2) does not exist.

Given that f(x)=x^2-6 and g(x)=3x+4, find (f-g)(-2), if it exists. Select the correct choice below and, if necessary, fill in the answer box to complete your choice. A. (f-g)(-2)= (Simplify your answer.) B. The value for (f-g)(-2) does not exist.
Transcript text: Given that $f(x)=x^{2}-6$ and $g(x)=3 x+4$, find $(f-g)(-2)$, if it exists. Select the correct choice below and, if necessary, fill in the answer box to complete your choice. A. $(f-g)(-2)=$ $\square$ (Simplify your answer.) B. The value for $(f-g)(-2)$ does not exist.
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Solution

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Solution Steps

Step 1: Identify the operation

The operation to perform is subtraction.

Step 2: Compute $f(a)$ and $g(a)$

Evaluating $f(a)$ gives -2 and evaluating $g(a)$ gives -2.

Step 3: Apply the operation

Applying the operation: $f(a) - g(a) = -2 + 2 = 0.$

Final Answer: The value of $(f \circ g)(a)$ is 0.

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