Question

suppose f(x) = (4/5)x^2 + cosx for x≥0 and g is the inverse of f. find g'(1.5) to the nearest thousandth.


would I just swap x and y and then find the derivative of that equation to find g'(x) and then plug in g'(1.5)? When I swapped x and y I got x=(4/5)y^2 + cosy and then do I do implicit differentiation? I suck at implicit differentiation so I'm stuck already :(

Answer 1

if g(x) = f^{^-1}(x) then
if f(a) = b then g'(b) = 1/f'(a)