Question

The table above gives values of the differentiable functions f and g, and f', the derivative of f, at selected values of x. If g(x) = f^-1(x), what is the value of g'(4) ?

(A) -1/3 (B) -1/4 (C) -3/100 (D) 1/4 (E) 1/3

Answer 1

B

Explanation:

i just need points

Answer 2

g'(4) is found using the inverse function rule. Given that g(x) = f^(-1)(x), the derivative of the inverse function at x = 4 is (g^(-1))'(4) = 1/3.

The correct answer is (E) 1/3.

Given values:

x: -4, f(x): 0, g(x): -9, f'(x): 5

x: -2, f(x): 4, g(x): -7, f'(x): 4

x: 0, f(x): 6, g(x): -4, f'(x): 2

x: 2, f(x): 7, g(x): -3, f'(x): 1

x: 4, f(x): 10, g(x): -2, f'(x): 3

We are asked to find g'(4), which is the derivative of g(x) at x = 4.

Identify the point where x = 4. At this point, f(x) = 10, and f'(x) = 3.

Since g(x) is the inverse function of f(x), g(10) = 4.

Now, apply the formula g'(x) = 1 / f'(g(x)) and substitute x = 10:

g'(4) = 1 / f'(g(10)) = 1 / f'(4) = 1 / 3

So, the calculation shows that g'(4) = 1/3. The correct answer is (E).