1) i) For the following functions, find the Inverse function. ii) A point (a,b)

Question

1)
i) For the following functions, find the Inverse function.

ii) A point (a,b) on the curve is given for each function. Find the slope of the function at the point (a,b).

iii) 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).

iv) Are the answers in parts ii and iii reciprocals? Graph the functions together, also plotting the graph y=x on the same set of axes to show that they are inverses of each other.

A.) f(x) = (x^2/3)+1 x?0
(a,b) = (1,2)

B.) f(x) = 3(fifthroot(2x-1))

(a,b) = (1/2,0)

C.) f(x) = x-3/x
(a,b) = (1,-2)

2) Time to think: Given what you know about relative extrema and Inverse functions, does it follow that if a maximum or minimum exists at a point (a,b) for a function, will the extrema exist for the Inverse function at the point (b,a)? Why or why not? You may experiment with the above functions if you wish, or choose another function...

Explanation / Answer

1) a) slope of given function at given point = 2/3 inverse function = y=(x-1)^(3/2) = (x-1)^1.5 b) slope of given function at given point = infinity = at this point tangent to this curve is parallel to y axis invesrse funtion = y = (x/3)^5 + 1 c) slope of given function at given point = 4 inverse function = y ={ X - (X^2 + 12)^.5 } /2 2)yes beacause inverse fucntion will be the image of original function with respect to line y=x

Related Questions

Navigate

• Browse (All)
• Browse 1
• Subjects

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.