Given the functions fx x24 and gx squareroot x2 3 1 find

Given the functions f(x) = x^2-4 and g(x) = squareroot x^2 + 3 + 1, find f(g(x)). Select one. A. f(g(x)) = squareroot x^2 - 8x+19+1 B. f(g(x)) = x^2 + 2squareroot x^2 + 3 C. f(g(x)) = x^2 D. f(g(x)) = x^2 + squareroot x^2 + 3 -3

Solution

Answer:-

Option (B) is the correct answer.

According to the statement

f(x) = x^2 -4

and

g(x) = (x^2 +3)^1/2 +1

we can easily find

f{g(x)}.

f{g(x)} = {(x^2 +3)^1/2 +1 + 2(x^2 +3)^1/2 -4

f{g(x)} = x^2 + 2( x^2 +3)^1/2

is the required solution.

So option (B) is the correct answer.