Question

Let f(x)=x-3 and g(x)=x+1(fg)(0)=?

Answer 1

Given:

The functions given are,

`\begin{gathered} f(x)=x-3 \\ g(x)=x+1 \end{gathered}`

Required:

To find the value of

`(fg)(0)`

Step-by-step explanation:

We have two given functions as:

`\begin{gathered} f(x)=x-3 \\ g(x)=x+1 \end{gathered}`

Therefore, the product of two functions is given by,

`\begin{gathered} (fg)(x)=f(x)\cdot g(x) \\ \Rightarrow(fg)(x)=(x-3)\cdot(x+1) \\ \Rightarrow(fg)(x)=x^2+x-3x-3 \\ \Rightarrow(fg)(x)=x^2-2x-3 \end{gathered}`

Thus, the value of the product of the functions at x = 0 is,

`\begin{gathered} (fg)(0)=(0)^2-2\cdot(0)-3 \\ \Rightarrow(fg)(0)=0-0-3 \\ \Rightarrow(fg)(0)=-3 \end{gathered}`

Final Answer:

The value of the product of the functions at x = 0 is,

`(fg)(0)=-3`