a logarithmic child function has domain of (-2, ∞). what is the range of the exponential child function that is its inverse?a.(-2, ∞)b.(2, ∞)c.(-∞, -2)d.(-∞, 2)

The logarithmic function has a domain of \((-2, \infty)\), which means its input values are greater than \(-2\). Since the exponential function is the inverse of the logarithmic function, its range will be the same as the domain of the logarithmic function.

Thus, the range of the exponential child function (inverse of the logarithmic function) is \((-2, \infty)\).

Therefore, the correct answer is:

**a. (-2, ∞)**

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Here are 5 related questions:
1. What is the general form of a logarithmic function?
2. How do you determine the domain and range of an exponential function?
3. What is the inverse relationship between logarithmic and exponential functions?
4. How does shifting a logarithmic function affect its domain?
5. What happens to the range if a logarithmic function has a vertical translation?

**Tip:** When finding the range of a function, remember that it's the set of possible output values for the given domain of its inverse.

A logarithmic child function has domain of (-2, ∞). What is the range of the exponential child function that is its inverse? a.(-2, ∞) b.(2, ∞) c.(-∞, -2) d.(-∞, 2)

Learn how to determine the range of an exponential function that is the inverse of a logarithmic function with a domain of (-2, ∞). This solution explores key mathematical concepts like logarithmic and exponential functions, inverse functions, and the relationship between their domain and range. Ideal for high school students in Grades 10-12.

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