Operations on Functions: f(x) = x and g(x) = x

Math Problem Statement

Find f + g,

f − g,

fg, and f/g and their domains. f(x) = x, g(x) =

x Find (f + g)(x).

Find the domain of (f + g)(x). (Enter your answer using interval notation.)

Find (f − g)(x).

Find the domain of (f − g)(x). (Enter your answer using interval notation.)

Find (fg)(x).

Find the domain of (fg)(x). (Enter your answer using interval notation.)

Find

f g

(x).

Find the domain of

f g

(x). (Enter your answer using interval notation.)

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Solution

It looks like you want to perform operations on two functions, $f(x)$ and $g(x)$ , but the expression for $g(x)$ wasn't fully given. You mentioned that $f(x) = x$ , but I don't see what $g(x)$ is. Could you please provide the full expression for $g(x)$ ?

Once I have that, I'll be able to help you find:

$f + g$
$f - g$
$f \cdot g$ (or $fg$ )
$\frac{f}{g}$ (or $f/g$ )

Also, I’ll calculate their domains and give the interval notation for each one.

Looking forward to your response!

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Math Problem Analysis

Mathematical Concepts

Functions
Operations on Functions
Domain of a Function

Formulas

f + g
f - g
f * g
f / g

Theorems

Domain of sum of functions
Domain of difference of functions
Domain of product of functions
Domain of quotient of functions

Suitable Grade Level

Grades 9-12

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