THE ANSWER I GOT FOR THIS WAS NOT THOROUGH ENOUGH BEFORE SO I AM OFFERING MORE P

Question

THE ANSWER I GOT FOR THIS WAS NOT THOROUGH ENOUGH BEFORE SO I AM OFFERING MORE POINTS!

1) For the following functions, find the Inverse function. Show all calculations.

2) A point (a,b) on the curve is given for each function. Find the slope of tangent line to the function at the point (a,b), by computing the derivative. Show all calculations.

3) The point (b,a) should be on the curve of the Inverse function. Is it? Find the slope of the Inverse function at the point (b,a). Show all calculations.

Explanation / Answer

a ) f(x) = x^4/5 - 1 x>= 0

using the formula f(f^-1 (x) ) = x ; let f^-1(x) = y

we get y^4/5 - 1 = x

y^4/5 = x + 1

y = (x+1)^5/4

inversse of f(x) = (x+1)^ 5/4

slope of tangent at (a,b) = f'(x) at x = a

f'(x) = 5/4*(x+1)^1/4

slope of tangent = f'(a) = 5/4*(2)^1/4 = 1.486

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