Question

Find the indicated values of the function: g(x) = -2x^(-1/3x+4) (check your answer by using the table feature of a calculator).

a) g(4)
b) g(-2)
c) g(sqrt(3))
d) N/A (function is undefined for given values)

Answer 1

To find the indicated values of the function g(x) = -2x^(-1/3x+4), we substitute the given values into the function and simplify. For g(4), g(-2), and g(sqrt(3)), we find -1/8, -1, and -2/cuberoot(3) as the respective values.

Step-by-step explanation:

To find the indicated values of the function g(x) = -2x^(-1/3x+4), we need to substitute the given values into the function and simplify.

a) g(4): We substitute x=4 into the function: g(4) = -2(4)^(-1/3*4+4). Simplifying, we get g(4) = -2(4)^(-4/3) = -2/((4)^(4/3)) = -2/(cuberoot(4^4)) = -2/16 = -1/8.

b) g(-2): We substitute x=-2 into the function: g(-2) = -2(-2)^(-1/3*(-2)+4). Simplifying, we get g(-2) = -2(-2)^(2/3) = -2/(cuberoot((-2)^2)) = -2/(cuberoot(4)) = -2/2 = -1.

c) g(sqrt(3)): We substitute x=sqrt(3) into the function: g(sqrt(3)) = -2(sqrt(3))^(-1/3*sqrt(3)+4). Simplifying, we get g(sqrt(3)) = -2(sqrt(3))^(-sqrt(3)/3+4) = -2/(sqrt(3))^(sqrt(3)/3) = -2/(cuberoot((sqrt(3))^(sqrt(3)))) = -2/cuberoot(3).