Question

Given F(x) = x² + 1 and g(x) = √(x+3), h(x) = f(g)(x), find h(x):

A) h(x) = x + 4
B) h(x) = x² + 4
C) h(x) = √(x² + 4)
D) h(x) = √(x+4)

Answer 1

To find h(x), we substitute g(x) into f(x) to get h(x) = f(g(x)) = (g(x))^2 + 1. Simplifying this gives us h(x) = x + 4, so the correct answer is A) h(x) = x + 4.

Step-by-step explanation:

To find h(x), which is f(g(x)), we first apply the function g to x and then apply the function f to the result of g(x). Starting with g(x) = √(x+3), we plug this into f(x) = x² + 1 to yield:

h(x) = f(g(x)) = (g(x))² + 1

Substituting g(x) into the equation:

h(x) = (√(x+3))² + 1

The square of the square root simply gives us the argument of the square root:

h(x) = x + 3 + 1

So we simplify:

h(x) = x + 4

Therefore, the correct choice is A) h(x) = x + 4.