Question

For which pairs of functions is (f⋅g)(x)=x?

A.f(x)=x^2 and g(x)= 1/x
B.f(x)=x and g(x)=2−3x
C.f(x)=3 and g(x)=x−2
D. f(x)=x−2 and g(x)=−3x+2

Answer 1

The correct pair of functions where (f⋅g)(x)=x is A: f(x)=x² and g(x)= 1/x, since multiplying these functions yields x.

Step-by-step explanation:

We are tasked with finding which pairs of functions satisfy the condition (f⋅g)(x)=x. Let's evaluate each option given:

• A. f(x)=x² and g(x)= 1/x: When we multiply these functions together we get (f⋅g)(x)=x²∙(1/x)=x. This pair satisfies the condition and (f⋅g)(x) indeed equals x.
• B. f(x)=x and g(x)=2−3x: When we multiply these functions together we get (f⋅g)(x)=x∙(2−3x)=2x∙3x², which does not equal x.
• C. f(x)=3 and g(x)=x−2: When we multiply these functions we get (f⋅g)(x)=3∙(x−2)=3x−6 which does not equal x.
• D. f(x)=x−2 and g(x)=−3x+2: When we multiply these functions we get (f⋅g)(x)=(x−2)∙(−3x+2)=−6x²+4x+6x−4 which does not equal x.

Therefore, the only correct pair is A: f(x)=x² and g(x)= 1/x.