Question

If g(x) is the inverse function of f(x) and f ' (x)= 1/ 1+x⁴, then g ′(x) is

Answer 1

If g(x) is the inverse function of f(x) and f ' (x)= 1/ 1+x⁴, then g ′(x) is 1+x⁴.

Step-by-step explanation:

If g(x) is the inverse function of f(x) and f ' (x)= 1/ 1+x⁴, then g ′(x) is

To find g'(x), we can use the inverse function rule, which states that if f(x) and g(x) are inverses, then the derivative of g(x) is equal to the reciprocal of the derivative of f(x). So, to find g'(x), we need to find the derivative of f(x) and take its reciprocal:

f'(x) = 1/ (1+x⁴)

g'(x) = 1/f'(x)

Therefore, g'(x) = 1/ (1/ (1+x⁴)) = 1+x⁴.