The value of f(g(x)) is x^2 + 1/x
How to determine the value
A function is an expression that describes the relationship between an independent variable and dependent variable.
Given the functions;
f(x) =
[tex] \sqrt[3]{x} [/tex]
g(x) =
[tex] \frac{ x+ 1}{ {x}^{3} } [/tex]
How to determine the function
Substitute the value do x as the value of the function g(x)
f(g(x)) =
[tex] \sqrt[3]{ \frac{x + 1}{ {x}^{3} } } [/tex]
Find the cube root of the expression
f(g(x)) =
[tex] \frac{ {x}^{3} + {1}^{3} }{x} [/tex]
Find the cube of the values
f(g(x)) =
[tex] \frac{ {x}^{3} + 1 }{x} [/tex]
Divide through by x, we have;
f(g(x)) = x^2 + 1/x
Thus, the value of f(g(x)) is x^2 + 1/x
Learn more about functions here:
https://brainly.com/question/2328150
#SPJ1
