Question

Find (f∘g)(x) and give the domain.

f(x)=√x+10 and g(x)=12x−26
A. (f∘g)(x)=4√3x−4√; [−4/3,[infinity])
B .(f∘g)(x)=4√3x−4; [4/3,[infinity])
C. (f∘g)(x)=2√3x−4; [4/3,[infinity])
D. (f∘g)(x)=2√3x−4; [−4/3,[infinity])

Answer 1

To find (f∘g)(x), substitute g(x) into f(x) and simplify the expression. The answer is √(12x - 16) and the domain is (-∞, ∞).

Step-by-step explanation:

To find (f∘g)(x), we need to substitute g(x) into f(x) and simplify the expression. First, substitute g(x) into f(x):

f(g(x)) = √(g(x) + 10) = √(12x - 26 + 10) = √(12x - 16)

So, (f∘g)(x) = √(12x - 16).

The domain of (f∘g)(x) is determined by the domain of g(x), which is all real numbers since there are no restrictions. Therefore, the domain of (f∘g)(x) is (-∞, ∞).