91Ó°ÊÓ

We have given,

$f\left(x\right)=-x and g\left(x\right)=2x-4$

A function which is depends on any other function we can call it as composite function.

$\left(f ∘ g\right)\left(x\right)=f\left(g\left(x\right)\right)$

Domainis the set of all input values where function is well defined and objective.

We have given,

$f\left(x\right)=-x and g\left(x\right)=2x-4$

Using definition of the composite function,

$$\begin{gathered} (f∘g)\left(x\right)=f\left(g\right(x\left)\right) \\ =f(2x-4) \\ =-(2x-4) \\ =-2x+4 \end{gathered}$$

We have given functions f and g both are polynomial functions so the domain of both functions is set of real numbers.

Therefore domain of the composite function is also the set of real numbers.

Domain:$\left(-∞,∞\right)$

Hence, composite function of the functions $f\left(x\right)=-x and g\left(x\right)=2x-4$is $\left(f ∘ g\right)=-2x+4$and domain is$\left(-∞,∞\right)$.

We have given,

$f\left(x\right)=-x and g\left(x\right)=2x-4$

Using definition of the composite function,

$$\begin{gathered} \left(g∘f\right)\left(x\right)=g\left(f\right(x\left)\right) \\ =g(-x) \\ =2(-x)-3 \\ =-2x-3 \end{gathered}$$

We have given functions f and g both are polynomial functions so the domain of both functions is set of real numbers.

Therefore domain of the composite function is also the set of real numbers.

Domain:$\left(-∞,∞\right)$

Hence, composite function $g∘f$of the functions$f\left(x\right)=-x and g\left(x\right)=2x-4$is$g∘f=-2x-3$and domain of the function is$\left(-∞,∞\right)$.

We have given,

$f\left(x\right)=-x and g\left(x\right)=2x-4$

Using definition of the composite function,

$$\begin{gathered} (f∘f)\left(x\right)=f\left(f\right(x\left)\right) \\ =f(-x) \\ =-(-x) \\ =x \end{gathered}$$

We have given functionsf and g both are polynomial functions so the domain of both functions is set of real numbers.

Therefore domain of the composite function is also the set of real numbers.

Domain:$\left(-∞,∞\right)$

Hence, composite function of $f\left(x\right)=-x $with itself is$f∘f=x$and domain of the function is,$\left(-∞,∞\right)$.

We have given,

$f\left(x\right)=-x and g\left(x\right)=2x-4$

Using definition of the composite function,

$$\begin{gathered} (g∘g)\left(x\right)=g\left(g\right(x\left)\right) \\ =g(2x-4) \\ =2(2x-4)-4 \\ =4x-8-4 \\ =4x-12 \end{gathered}$$

We have given functions f and g both are polynomial functions so the domain of both functions is set of real numbers.

Therefore domain of the composite function is also the set of real numbers.

Domain:$\left(-∞,∞\right)$

Hence, composite function of the functions $f\left(x\right)=-x and g\left(x\right)=2x-4$is

$g∘g=4x-12$and domain of the composite function is,$\left(-∞,∞\right)$.