Perform the requested operation or operations. Find the domain of each.
-$$f ( x ) = 2 x + 7 , g ( x ) = 6 x ^ { 2 }$$
Find $( \mathrm { fg } ) ( \mathrm { x } )$.
A) $12 x ^ { 3 } + 42 x ^ { 2 }$; domain: $( - \infty , \infty )$
B) $12 x + 42$; domain: $( - \infty , \infty )$
C) $6 x ^ { 2 } + 2 x + 7$; domain: $( - \infty , \infty )$
D) $12 x ^ { 2 } + 42 x$; domain: $( - \infty , \infty )$

Question

Quizplus · Accepted Answer

The product $(fg)(x)$ means $f(x) \times g(x)$, which is $(2x + 7) \times (6x^2)$. Multiplying these gives $12x^3 + 42x^2$. Both $f(x)$ and $g(x)$ are polynomials, so their domains are all real numbers, $(- \infty , \infty )$.

Perform the Requested Operation or Operations f(x)=2x+7,g(x)=6x2f ( x ) = 2 x + 7 , g ( x ) = 6 x ^ { 2 }f(x)=2x+7,g(x)=6x2

Perform the Requested Operation or Operations $f ( x ) = 2 x + 7 , g ( x ) = 6 x ^ { 2 }$