Question

Given f(x)=3x+5 and g(x)=2x^2-4x+8, find f(x)•g(x)

Answer 1

The functions are given below as

`f\lparen x)=3x+5,g\lparen x)=2x^2-4x+8`

Concept:

To figure out f(x0.g(x), we will use the formula below

`f\mleft(x\mright).g\mleft(x\mright)=f\mleft(x\mright)* g\mleft(x\mright)`

By substituting the values, we will have

`f\mleft(x\mright).g\mleft(x\mright)=\left(3x+5\right?\left(2x^2-4x+8\right?`

By expanding the brackets, we will have

`\begin{gathered} f\mleft(x\mright).g\mleft(x\mright)=3x\left(2x^2-4x+8\right?+5\left(2x^2-4x+8\right? \\ f\mleft(x\mright).g\mleft(x\mright)=6x^3-12x^2+24x+10x^2-20x+40 \\ f\mleft(x\mright).g\mleft(x\mright)=6x^3-12x^2+10x^2+24x-20x+40 \\ f\mleft(x\mright).g\mleft(x\mright)=6x^3-2x^2+4x+40 \end{gathered}`

Hence,

The final answer is

`f\mleft(x\mright).g\mleft(x\mright)=6x^3-2x^2+4x+40`