If 𝑓(𝑥)=𝑥2+3 and 𝑔(𝑥)=7𝑥−3, find 𝑓(𝑔(𝑥)).𝑓(𝑔(𝑥))

To find the composition of the functions 𝑓(𝑔(𝑥)), we need to substitute 𝑔(𝑥) into 𝑓(𝑥).

Step 1: Write down the function 𝑓(𝑥)=𝑥²+3

Step 2: Substitute 𝑔(𝑥) into 𝑓(𝑥). So wherever there is an 'x' in 𝑓(𝑥), we replace it with 𝑔(𝑥).

This gives us 𝑓(𝑔(𝑥)) = (7𝑥-3)² + 3

Step 3: Expand the square in the equation.

(7𝑥-3)² = 49𝑥² - 42𝑥 + 9

So, 𝑓(𝑔(𝑥)) = 49𝑥² - 42𝑥 + 9 + 3

Step 4: Simplify the equation by adding the constants.

So, 𝑓(𝑔(𝑥)) = 49𝑥² - 42𝑥 + 12

So the composition of the functions 𝑓(𝑔(𝑥)) is 49𝑥² - 42𝑥 + 12.