A function is defined by (h : x to 2 – frac{1}{2x – 3}, x neq frac{3}{2}). Find (h^-1), the inverse of h.
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A.
(frac{3x – 4}{2x – 7}, x neq frac{7}{2}) -
B.
(frac{3x – 7}{2x – 4}, x neq 2) -
C.
(frac{2x – 7}{4x – 3}, x neq frac{3}{4}) -
D.
(frac{4x – 7}{2x – 4}, x neq 2)
Correct Answer: Option B
Explanation
(h : x to 2 – frac{1}{2x – 3})
(h(x) = frac{2(2x – 3) – 1}{2x – 3} = frac{4x – 7}{2x – 3})
Let x = h(y)
(x = frac{4y – 7}{2y – 3})
(x(2y – 3) = 4y – 7 implies 2xy – 4y = 3x – 7)
(y = frac{3x – 7}{2x – 4})
(h^{-1}(x) = frac{3x – 7}{2x – 4})