Today we will be discussing composition of functions. That is denoted by f composed of g of x. Again, let us repeat. Composed of g of x. And that is equal to f of g of x.
So how... How we are going to use this? Paano natin ito gagamitin? Let's say, we have g of x is equal to 5x plus 3 and f of x is equal to 2x squared plus 1 So, start muna tayo sa basic. Tanggalin natin yung square.
Yan lang muna. Again. g of x is equal to 5x plus 3, and f of x is equal to 2x squared plus 1. Find f, or compose of g, of x. Yan.
Hanapin natin siya. So, alam natin, may compositional functions, si f of g of x, ay equal siya kay f of g of x. So, ano ba yung uunahin muna natin nasa loob ng parentheses natin? Si g of x.
So, ano yung value ni g of x? Tingnan ng given. So, f of g of x natin ay 5x plus 3. Ayan.
Sinubstitute lang natin yung value ni g of x. Next, meron tayong f of 5x plus 3. Ito ngayon, yung 5x plus 3, isasubstitute natin dun sa value ni f of x. So we have 2 times, ang x daw natin ay 5x plus 3. So palitan natin si x na 5x plus 3. Then don't forget, meron tayong plus 1. So add natin ang plus 1. Then simplify na natin.
2 times 5x, that is 10x. 2 times 3, positive 6. Then copy, plus 1. So, final answer, 10x plus... 6 plus 1, 7. So ito ngayon, yung ating value ng f composed of g of x.
Ayan siya. Try pa natin ng isang example. Let's say, meron tayong F of x is equal to 5x squared minus x plus 4. Then g of x is equal to 2x minus 1. Find g composed of f of x.
Yan yung hanapin natin. So, solve natin. Alam natin na ang g composed of f of x is equal to g of f of x.
So, magkatabi, mas malapit si x kay x. So, i-cookin natin. Nakukuha yung relationship nila? Okay. So, si f of x, cookin natin yung value niya.
Sapsin natin dito. So we have g of, ang f of x daw natin ay 5x squared minus x plus 4. Okay? Now, g of 5x squared minus x plus 4. Meron tayong g of x.
Lahat ng x dito, expression natin, palitan natin dito. So we have 2 times, value natin, 5x squared minus x plus 4 then minus 1. Distribute. So 2 times 5, 10x squared. 2 times negative x, negative 2x.
2 times 4, positive 8. And copy, negative 1. This time, combine like terms. So, copy 10x squared, minus 2x. 8 minus 1, that is 7. So, ito na ngayon yung value ng ating g-composite of x. So ganyan ang magsmove ng composition of functions.