What is the value of g(f(sqrt(5))) if f(x) = cbrt(x^2 - 4) and g(x) = x^3 - 3x?

To find the value of g(f(sqrt(5))), we need to first evaluate f(sqrt(5)) using the given function f(x) = cbrt(x^2 - 4).

1. Calculate f(sqrt(5)):

• Start by computing sqrt(5)^2:

[

sqrt(5)^2 = 5

]

• Next, substitute this back into the function:

[

f(sqrt(5)) = cbrt(5 - 4) = cbrt(1)

]

• The cube root of 1 is:

[

cbrt(1) = 1

]

2. Now that we have f(sqrt(5)) = 1, we substitute this value into the function g(x):

• The function g(x) is defined as g(x) = x^3 - 3x. So, we calculate:

[

g(1) = 1^3 - 3 \cdot 1

]

• Evaluating this expression gives:

[

g(1) = 1 - 3 = -2