Question

G(x)=x^3 find (g^-1 of g^-1)(-4)

Answer 1

To find (g^-1 of g^-1)(-4), we apply the cube root twice to -4, and get (-4)^(1/9) as the final result.

Step-by-step explanation:

To find (g-1 of g-1)(-4), we first need to understand the function g(x) = x3 and its inverse, g-1(x). The inverse function essentially 'undoes' what the original function does. In this case, the inverse function of g(x) would be the cube root function, since taking the cube root is the inverse operation of cubing a number. So, g-1(x) is equivalent to ∛x.

Now, to find (g-1 of g-1)(-4), we will apply the inverse function to -4 twice:

1. First, find g-1(-4), which is ∛(-4). Since the cube root of a negative number is negative, g-1(-4) = -∛4.
2. Next, we apply the inverse function again to -∛4, so g-1(-∛4) is the cube root of the previous result, ∛(-∛4).
3. By simplifying, we find that the cube root of the cube root of -4 is -4 to the power of one-third (which is the cube root), and then another one-third: (-4)1/9.

Therefore, the result of (g-1 of g-1)(-4) is (-4)1/9.