Find the Domain h-1x

Problem

h(x)=(x−1)/(x+2)

Solution

1. Identify the function h(x) and recognize that the task is to find the domain of its inverse, h(x)(−1)

2. Recall the property that the domain of an inverse function h(x)(−1) is equal to the range of the original function h(x)

3. Determine the range of h(x) by identifying the horizontal asymptote of the rational function.

4. Compare the degrees of the numerator and denominator; since both are degree 1, the horizontal asymptote is the ratio of the leading coefficients.

5. Calculate the horizontal asymptote as y=1/1=1

6. Conclude that the function h(x) can take any value except 1 meaning the range of h(x) is {[y∈ℝ,y≠1]}

7. State the domain of h(x)(−1) based on the range of h(x)

Final Answer

Domain of *h(x)(−1)={[x∈ℝ,x≠1]}

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