Function $\boldsymbol{f}$ is defined by $\boldsymbol{f}(\boldsymbol{x})=-\boldsymbol{a}^{\boldsymbol{x}}+\boldsymbol{b}$, where $\boldsymbol{a}$ and $\boldsymbol{b}$ are constants. In the $x y$-plane, the graph of $\boldsymbol{y}=\boldsymbol{f}(\boldsymbol{x})-\mathbf{1 2}$ has a $y$-intercept at $(\mathbf{0},-\frac{\mathbf{1 2}}{2})$. The product of $\boldsymbol{a}$ and $\boldsymbol{b}$ is $\frac{\boldsymbol{a} \boldsymbol{b}}{\boldsymbol{1}}$. What is the value of $\boldsymbol{a}$ ?
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Answer

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Step 1
: Use the given information about the y-intercept to find the value of $b$.

Therefore, $b = 0$.

Step 2
: Use the product of $a$ and $b$ to find the value of $a$.

However, without any additional information, we cannot determine the exact value of $a$.

Final Answer

The value of $a$ cannot be determined with the given information.