Question

Find the inverse function of f. f(x) = 49 x2 , x > 0

Answer 1

f^(-1)(x) = sqrt(x/49)

Explanation:

To find the inverse function of f(x) = 49x^2, we need to solve for x in terms of f(x) and then interchange x and f(x).

f(x) = 49x^2

f(x)/49 = x^2

sqrt(f(x)/49) = x (since x > 0)

So, the inverse function of f(x) is:

f^(-1)(x) = sqrt(x/49)

Note that the domain of f^(-1) is x ≥ 0, since x must be positive for the inverse function to be defined. Also, note that f(f^(-1)(x)) = f(sqrt(x/49)) = 49(sqrt(x/49))^2 = 49(x/49) = x, and f^(-1)(f(x)) = sqrt(f(x)/49) = sqrt(49x^2/49) = x. Therefore, f^(-1) is the inverse function of f.