91Ó°ÊÓ

We have given,

$f\left(x\right)=x^2+1, g\left(x\right)=2x^2+3$

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,

$f\left(x\right)=x^2+1, g\left(x\right)=2x^2+3$

Using definition of the composite function,

localid="1647491500448" $$\begin{gathered} f ∘ g=f\left(g\left(x\right)\right) \\ =f\left(2x^2+3\right) \\ ={(2x^2+3)}^2+1 \\ =4x^4+12x^2+10 \end{gathered}$$

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 $f\left(x\right)=x^2+1, g\left(x\right)=2x^2+3$is$f ∘ g=4x^4+12x^2+10$and domain is$\left(-∞,∞\right)$.

We have given,

$f\left(x\right)=x^2+1, g\left(x\right)=2x^2+3$

Using definition of the composite function,

$$\begin{gathered} g ∘ f=g\left(f\left(x\right)\right) \\ =g\left(x^2+1\right) \\ =2{\left(x^2+1\right)}^2+3 \\ =2x^4+4x^2+5 \end{gathered}$$

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, composition of the functions $f\left(x\right)=x^2+1, g\left(x\right)=2x^2+3$is $g ∘ f=2x^4+4x^2+5$and domain is$\left(-∞,∞\right).$

We have given,

$f\left(x\right)=x^2+1, g\left(x\right)=2x^2+3$

Using definition of the composite function,

$$\begin{gathered} f ∘ f=f\left(f\left(x\right)\right) \\ =f\left(x^2+1\right) \\ ={\left(x^2+1\right)}^2+1 \\ =x^4+2x^2+2 \end{gathered}$$

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 function $f\left(x\right)=x^2+1, g\left(x\right)=2x^2+3$is $f ∘ f=x^4+2x^2+2$and domain is$\left(-∞,∞\right).$

We have given,

$f\left(x\right)=x^2+1, g\left(x\right)=2x^2+3$

Using definition of the composite function,

$$\begin{gathered} g ∘ g=g\left(g\left(x\right)\right) \\ =g\left(2x^2+3\right) \\ =2{\left(2x^2+3\right)}^2+3 \\ =8x^4+24x^2+21 \end{gathered}$$

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 function $f\left(x\right)=x^2+1, g\left(x\right)=2x^2+3$is$g ∘ g=8x^4+24x^2+21$and domain of the function is$\left(-∞,∞\right).$