ON (-1,1) the function f(x)=1+x²+tan(πx/2) has an inverse g. Find the value of g'(1). Please help me?
There was a hint given too. it said find the value of f(0), but i don't even know why that is relevant. Can you please help me with this i'm not too sure how to do this problem at all. Your help will be greatly appreciated.
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f(0) = 1 => g(1) = 0
f'(0) = π/2
g'(1) = 1/f'(0) = 2/π
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Ideas: dx/dy = 1/(dy/dx). Here y = f(x), x = g(y)
The domain and range of a function and its inverse are swapped. The domain of the function is the range of the inverse and vice versa. Since f(0)=1 we can know that g(1)=0 because 1, the range of f(x), is put into g(x) as the domain and 0, the domain of f(x), becomes the range for g(x).