Answer:
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
