Find (fg)(x). $$f ( x ) = x ^ { 2 } , g ( x ) = 7 x - 7$$
A) $$7 x ^ { 3 } + 7 x ^ { 2 }$$
B) $7 x ^ { 3 } - 7 x ^ { 2 }$
C) $7 x ^ { 2 } - 7 x ^ { 3 }$
D) $7 x ^ { 2 } + 7 x ^ { 3 }$
E) $7 x - 7 x ^ { 2 }$

Question

Find (fg)(x).​ $$f ( x ) = x ^ { 2 } , g ( x ) = 7 x - 7$$ ​
A) $$7 x ^ { 3 } + 7 x ^ { 2 }$$
B) $7 x ^ { 3 } - 7 x ^ { 2 }$
C) $7 x ^ { 2 } - 7 x ^ { 3 }$
D) $7 x ^ { 2 } + 7 x ^ { 3 }$
E) $7 x - 7 x ^ { 2 }$

Quizplus · Accepted Answer

The composition (fg)(x) means applying g(x) to f(x), or f(g(x)). Substituting g(x) = 7x - 7 into f(x) = x^2 gives f(g(x)) = (7x - 7)^2. Expanding this, we get 49x^2 - 98x + 49. However, the correct operation for (fg)(x) is actually multiplying f(x) by g(x), not substituting. Therefore, (fg)(x) = (x^2)(7x - 7) = 7x^3 - 7x^2, which matches option B.

Find (Fg)(x) f(x)=x2,g(x)=7x−7f ( x ) = x ^ { 2 } , g ( x ) = 7 x - 7f(x)=x2,g(x)=7x−7

Find (Fg)(x) $f ( x ) = x ^ { 2 } , g ( x ) = 7 x - 7$