Can someone answer this for me asap ?

The expression which is equivalent to (f ° g)(x) is 3(x² + 1) + 2 ⇒ the 4th answer

Step-by-step explanation:

* Lets explain the meaning of the composition of functions

- Composition of functions is when one function is inside of an another

 function

# If g(x) and h(x) are two functions, then (g ° h)(x) means h(x) is inside

  g(x) and (h ° g)(x) means g(x) is inside h(x)

* Now lets solve the problem

∵ f(x) = 3x + 2

∵ g(x) = x² + 1

- We need to find (f ° g)(x), that means put g(x) inside f(x)

* Lets replace the x of f by the g(x)

∵ f(x) = 3x + 2

∵ g(x) = x² + 1

- Replace x of f by x² + 1

∴ f(x² + 1) = 3(x² + 1) + 2 ⇒ open the bracket

∴ f(x² + 1) = 3x² + 3 + 2 ⇒ add the like terms

∴ f(x² + 1) = 3x² + 5

∴ (f ° g)(x) = 3(x² + 1) + 2 OR 3x² + 5

* The expression which is equivalent to (f ° g)(x) is 3(x² + 1) + 2