Suppose f is a one-to-one function with f(2)=8 and f’(2)=4. what is the value of (f^-1)’(8)?

1/4

Step-by-step explanation:

The tangent line to f(x) at x=2 goes through the point (2, 8) and has slope 4.

The inverse function f⁻¹(x) is a reflection of the function f(x) across the line y=x. The corresponding tangent line will go through point (8, 2) and have slope 1/f'(2) = 1/4 at that point. That is, ...

(f⁻¹)'(8) = 1/f'(f⁻¹(8)) = 1/f'(2) = 1/4

step-by-step explanation:

in the absence of parentheses, i will have to make some assumptions:   i interpret your (3x+5/y^6)(4y^3/5)​ to mean:

3x + 5     4y^(3/5)       (3x + 5)(4)

* =

    y^6             1               y^(6-3/5)

if this is not what you expected, repost your question using parentheses to indicate whether you meant

4y^3

    or   4y^(3/5)

    5