Question

Given f(x)=√(2-12x) and g(x)=-5/x, find the following:
g⁰f(x)=____

Answer 1

To find the composition g⁰f(x), the value of f(x), which is the square root of (2-12x), is substituted into g(x). Since g(x) is -5/x, the result is -5 divided by the square root of (2-12x), giving the composition g⁰f(x) as -5/(√(2-12x)).

Step-by-step explanation:

The student asks to find the composition of the functions f and g, denoted as g⁰f(x). This means we need to evaluate g at the point f(x). Given f(x)=√(2-12x) and g(x)=-5/x, we will follow this process:

1. First, find f(x).
2. Then plug the value of f(x) into g as its argument.

Starting with f(x):

f(x) = √(2-12x)

Now, substitute f(x) into g(x):

g(f(x)) = g(√(2-12x)) = -5/(√(2-12x))

The composition of g and f, denoted as g⁰f(x), is thus -5/(√(2-12x)).