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Question:

If f(x) = x² - x + 5, x > 1/2, and g(x) is its inverse function, then g'(7) equals :

113

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13

Solution:

f(x) = x² - x + 5, x > 1/2
y = x² - x + 5
x² - x + 5 - y = 0
x = 1 ± √(1 + 4(y - 5))/2
g(x) = 1 ± √(1 + 4(x - 5))/2
g'(x) = 4 × 1/(2√(1 + 4(x - 5))) × 1/2
g'(x) = 1/√(1 + 4(x - 5))
g'(7) = 1/√(1 + 4(7 - 5)) = 1/√9 = 1/3