7. If $$ f(x)=\log 2^{x^{2}+4 x-5} $$ then, what is the domain of $$ \mathrm{f}(\mathrm{x}) $$ ?

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UpStudy AI · Accepted Answer

To determine the domain of the function $$ f(x) = \log \left( 2^{x^2 + 4x - 5} \right) $$, we need to ensure that the argument of the logarithm is positive because the logarithm is only defined for positive real numbers.

Let's analyze the argument inside the logarithm:

$$
2^{x^2 + 4x - 5}
$$

Since the base $$2$$ is a positive number and an exponential function with a positive base is always positive regardless of the exponent, the expression $$2^{x^2 + 4x - 5}$$ is always positive for all real values of $$x$$.

Therefore, the logarithm function is defined for all real numbers $$x$$ in this case.

**Domain of $$ f(x) $$:** All real numbers $$x$$.

**Final Answer:**

All real numbers are allowed. The domain of f  is all real numbers.
The domain of $$ f(x) $$ is all real numbers.

If then, what is the domain of ?

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