f(x) = x^5 + 2x^3 + x - 1

Question

Find f^-1 (3) and (f^-1)' (3)

f^-1 (3) = 1

(f^-1)' (3) = 1/12

Those are the answers, but I have no clue how my teacher got them.

Answer 1

y = x^5 + 2 x^3 + x - 1
exchange x and y

x = y^5 + 2 y^2 + y - 1
now use 3 for x
4 = y^5 + 2 y^2 + y
1 works for y

Answer 2

dy/dx = 5 x^4 + 6 x^2 + 1
but x is 1 here we know already
dy/dx = 5+6 + 1 = 12
interchange
dy/dx = 1/12

Answer 3

Thank You so much!

Answer 4

Actually I do have one question, how do we know that x is 1 already ???

Answer 5

remember 1 worked for y, so not it works for x :)