Question

For the given functions f and g, complete parts (a)-(h). For parts (a)-(d), also find the domain F(x) =x-2;g(x) =2x^2

Answer 1

We have the next two functions:

1.

`f(x)=x-2`

2.

`g(x)=2x^2`

(a) We must find (f + g) (x)

To find it we must use that

`(f+g)(x)=f(x)+g(x)`

Now, replacing the functions we obtain

`\begin{gathered} (f+g)(x)=x-2+2x^2 \\ \text{Organizing the terms} \\ (f+g)(x)=2x^2+x-2 \end{gathered}`

Then, the domain of f + g is

`\text{ The domain is }\mleft\lbrace x\mright|x\text{ is any real number}\}`

(b) We must find (f - g) (x)

To find it we must use that

`(f-g)(x)=f(x)-g(x)`

Now, replacing the functions we obtain

`\begin{gathered} (f-g)(x)=x-2-2x^2 \\ \text{ Organizing the terms} \\ (f-g)(x)=-2x^2+x-2 \end{gathered}`

Then, the domain of f - g is

`\text{The domain is }\lbrace x|x\text{ is any real number}\}`