overall accuracy: 85.3% record: 25 score: 24 if g(x)=f^(-1)(x), with f(4)=6 and g(4)=2, then g(4) equals…

overall accuracy: 85.3% record: 25 score: 24 if g(x)=f^(-1)(x), with f(4)=6 and g(4)=2, then g(4) equals 1/f(2) 1/g(2) 1/f(6) 1/g(6) high score board: overall refresh you must have at least 100 to be on the board. # name record answer submitting is not possible on this problem. just follow the instructions above.

overall accuracy: 85.3% record: 25 score: 24 if g(x)=f^(-1)(x), with f(4)=6 and g(4)=2, then g(4) equals 1/f(2) 1/g(2) 1/f(6) 1/g(6) high score board: overall refresh you must have at least 100 to be on the board. # name record answer submitting is not possible on this problem. just follow the instructions above.

Answer

Explanation:

Step1: Recall inverse - function derivative formula

If (g(x)=f^{-1}(x)), then (g^{\prime}(x)=\frac{1}{f^{\prime}(g(x))}).

Step2: Substitute (x = 4)

We want to find (g^{\prime}(4)). Using the formula (g^{\prime}(x)=\frac{1}{f^{\prime}(g(x))}), when (x = 4), we have (g^{\prime}(4)=\frac{1}{f^{\prime}(g(4))}).

Step3: Use the given value of (g(4))

Since (g(4)=2), then (g^{\prime}(4)=\frac{1}{f^{\prime}(2)}).

Answer:

A. (\frac{1}{f^{\prime}(2)})