QQuestionMathematics
QuestionMathematics
The one to one function h is defined below. h(2$)= 7x- 2 /x+ 1 Find h^- 1(x), where h^- 1 is the inverse of h. Also state the domain and range of h^- 1 in interval notation.
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Answer
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Step 1: Set the original function h(x) equal to y.
y = h(x) = \frac{7x-2}{x+1}
Step 2: To find the inverse function, switch x and y.
x = h^{-1}(y) = \frac{7y-2}{y+1}
Final Answer
The inverse function is: h^{- 1}(x) = \frac{2}{7 -x} The domain of h^{- 1}(x) is: (-\infty, 7) \cup (7, \infty) The range of h^{- 1}(x) is: (-\infty, \infty)
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