Question

given the functions, f(x)=x^2 and g(x)=x+2, perform the indicated operation. when applicable, state the domain restriction. f(g(x)​

Answer 1

h(g(x)) = x²+4x+4

Domain restriction =
`[-\infty, \infty]`

Explanation:

Given the functions h(x)=x^2 and g(x)=x+2, we are to find h(g(x)). To get the indicated operation we need to follow the steps;

Since the function in parenthesis g(x) = x+2

h(g(x)) can be written as h(x+2). Hence we are to look for the equivalent expression of h(x+2).

Since h(x) = x², h(x+2) can simply be gotten by simply replacing the variable x in h(x) as x+2 as shown;

h(x+2) = (g(x))²

h(x+2) = (x+2)²

We can open the bracket

h(x+2) = x²+4x+4

The domain restriction is the point where the function cannot exist for the value of x. The function can therefore exist on any real value R. The only domain restriction is at the interval
`[-\infty, \infty]`

Hence h(g(x)) is equivalent to x²+4x+4.