91Ó°ÊÓ

We have given,

$f\left(x\right)=x^2, g\left(x\right)=x^2+4$

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

$f ∘ g=f\left(g\left(x\right)\right)$

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

We have given,

$f\left(x\right)=x^2, g\left(x\right)=x^2+4$

Using definition of the composite function,

$$\begin{gathered} f ∘ g=f\left(g\left(x\right)\right) \\ =f\left(x^2+4\right) \\ ={\left(x^2+4\right)}^2 \\ =x^4+8x^2+16 \end{gathered}$$

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 $f\left(x\right)=x^2, g\left(x\right)=x^2+4$is$f ∘ g=x^4+8x^2+16$and domain of the function is$\left(-∞, ∞\right)$.

We have given,

$f\left(x\right)=x^2, g\left(x\right)=x^2+4$

Using definition of the composite function,

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

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 $f\left(x\right)=x^2, g\left(x\right)=x^2+4$is

$g ∘ f=x^4+4$and domain is$\left(-∞, ∞\right)$.

We have given,

$f\left(x\right)=x^2, g\left(x\right)=x^2+4$

Using definition of the composite function,

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

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 $f\left(x\right)=x^2, g\left(x\right)=x^2+4$is

$f ∘ f=x^4$and domain is$\left(-∞, ∞\right)$.

We have given,

$f\left(x\right)=x^2, g\left(x\right)=x^2+4$

Using definition of the composite function,

$$\begin{gathered} g ∘ g=g\left(g\left(x\right)\right) \\ =g\left(x^2+4\right) \\ ={\left(x^2+4\right)}^2+4 \\ =x^4+8x^2+20 \end{gathered}$$

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 the function $f\left(x\right)=x^2, g\left(x\right)=x^2+4$is $g ∘ g=x^4+8x^2+20$and domain is$\left(-∞, ∞\right)$