Question

What is the composite function f(g(x)) for the given functions f(x)=x²+3 and g(x)=√x−2?

A) f(g(x))=(√x−2)² +3

B) f(g(x))=(√x−2)² -3

C) f(g(x))=(√x+2)² +3

D) f(g(x))=(√x+2)² -3

Answer 1

The composite function f(g(x)) for the given functions f(x)=x²+3 and g(x)=√x−2 is (√x−2)² + 3.

Step-by-step explanation:

To find the composite function f(g(x)) for the given functions f(x)=x²+3 and g(x)=√x−2, we need to substitute the function g(x) into the function f(x). So, f(g(x)) = (g(x))² + 3. Since g(x) = √x−2, we have f(g(x)) = (√x−2)² + 3.

ANSWER: A) f(g(x))=(√x−2)² +3