Question

Consider these functions: f(x)=x²+1 and g(x)=2/x. Which polynomial is equivalent to (f∘g) (x)?

a) 2x²+1
b) 2x²-2
c) 2/x+1
d) 2/x²+1

Answer 1

Step-by-step explanation:

hello :

given : f(x)=x²+1 and g(x)=2/x

(f∘g) (x)= f(g(x))=f(2/x)

now put 2/x in f(x)

(f∘g) (x)= (2/x)²+1

(f∘g) (x)= 4/x²+1

Answer 2

The composition of functions (f∘g)(x) means applying the function g first and then applying the function f. To find (f∘g)(x), we substitute the expression of g(x) into f(x) and simplify to get 4/x² + 1 as the equivalent polynomial.

Step-by-step explanation:

The composition of functions (f∘g)(x) means applying the function g first and then applying the function f. To find (f∘g)(x), we first substitute the expression of g(x) into f(x).

Substituting, we get:
(f∘g)(x) = f(g(x)) = f(2/x) = (2/x)² + 1 = 4/x² + 1.

Therefore, the polynomial equivalent to (f∘g)(x) is 4/x² + 1, which is option (d).