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) into f(x), we get $f(g(x)) = f(7x - 7) = (7x - 7)^2$. Expanding this, we get $49x^2 - 98x + 49$, which does not match any of the options directly because I made an error in the explanation. The correct process is to multiply f(x) by g(x), resulting in $x^2(7x - 7) = 7x^3 - 7x^2$, 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) $f ( x ) = x ^ { 2 } , g ( x ) = 7 x - 7$