Question

Functions f(x) and g(x) are composed to form h(x) = sqrt(x ^ 3- 2) if f(x) = sqrt(x + 2) and g(x) =x^3+a. What is the value of a

Answer 1

Answer:-4 or D

Explanation:

Answer 2

Answer: a = -4

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) =
`\sqrt{x^(3)+a+2}`

`\sqrt{x^(3)-2} =\sqrt{x^(3)+a+2}`

Now, to find a, we separate equal terms:

1) Both are squared, so we can "eliminate" the square;

2) x³ = x³;

3)
`-2=a+2`

`a=-4`

For function composition h(x) = f(g(x)), the value of a is -4.