I can't figure out this problem, I know I have to find the derivative of 2x-4 first and then substitute f^-1(x) into (1/f(f^-1(x)), but I don't get how to do that for this problem since the derivative of it is 2 & there's no x. I don't know if that made any sense, haha. Please help though...I've tried this problem several times & I wanna be done with my homework already. The link below is the problem.
http://i50.tinypic.com/eq1sp.jpg
http://i50.tinypic.com/eq1sp.jpg
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What is the value of d/dx[f⁻¹(x)] when x=2, given that f(x) = 2x-4?
First, get f⁻¹(x):
f(x) = 2x-4
y = 2x-4 ← To get the inverse function of f, interchange
the variables and then solve for y.
So,
x = 2y-4
4+x = 2y
(4+x)/2 = y
y = ½ x + 2
f⁻¹(x) = ½ x + 2 ← Now, take the derivative of f⁻¹(x)
d/dx[f⁻¹(x)] = ½ ← The derivative is a constant.
This tells you that for all x, the derivative is ½.
Therefore,
d/dx[f⁻¹(2)] = ½ ← i.e. the derivative of f⁻¹ when x=2 is ½
ANSWER
½
Have a good one!
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What is the value of d/dx[f⁻¹(x)] when x=2, given that f(x) = 2x-4?
First, get f⁻¹(x):
f(x) = 2x-4
y = 2x-4 ← To get the inverse function of f, interchange
the variables and then solve for y.
So,
x = 2y-4
4+x = 2y
(4+x)/2 = y
y = ½ x + 2
f⁻¹(x) = ½ x + 2 ← Now, take the derivative of f⁻¹(x)
d/dx[f⁻¹(x)] = ½ ← The derivative is a constant.
This tells you that for all x, the derivative is ½.
Therefore,
d/dx[f⁻¹(2)] = ½ ← i.e. the derivative of f⁻¹ when x=2 is ½
ANSWER
½
Have a good one!
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