Respuesta :
Answer: a = -4
Step-by-step explanation: Function Composition is when two functions f(x) and g(x) result in another function h(x), such that h(x) = f(g(x)). In other words, put the result of one function into the other one.
In this situation,
h(x) = f(g(x))
which means
h(x) = f(x³+a)
h(x) = [tex]\sqrt{x^{3}+a+2}[/tex]
[tex]\sqrt{x^{3}-2} =\sqrt{x^{3}+a+2}[/tex]
Now, to find a, we separate equal terms:
1) Both are squared, so we can "eliminate" the square;
2) x³ = x³;
3) [tex]-2=a+2[/tex]
[tex]a=-4[/tex]
For function composition h(x) = f(g(x)), the value of a is -4.
