Is this function correct? (Not a homework Question)

[QuantumPixel]

I was bored and decide to make a function (yes, i am a bit weird). So I came up with this:

f(x)=2x+3
g(f)= f+2
w(g)=g²+3

x=2

f(2)=4+3
f(2)=7
g(7)=7+2
g(7)=9
w(9)=81+3
w(9)=82

Is those working outs correct or not? If it isn't could you tell me where i got it wrong?

 

[Gackhammer]

As long as you mean g(f(x)) and w(g(f(x))), then you have the right answer

 

[HallsofIvy]

Yes, what you have is correct. More generally, with f(x)= 2x+ 3, g(x)= x+ 2, and $w(x)= x^2+ 3$, $g(f(x)= (2x+ 3)+ 2= 2x+ 5$ and $w(g(f(x)))= (2x+ 5)^2+ 3= 4x^2+ 20x+ 28$.

Evaluating that at x= 2 gives 4(4)+ 20(2)+ 28= 16+ 40+ 28= 84.

 

[QuantumPixel]

As long as you mean g(f(x)) and w(g(f(x))), then you have the right answer

Yes, what you have is correct. More generally, with f(x)= 2x+ 3, g(x)= x+ 2, and $w(x)= x^2+ 3$, $g(f(x)= (2x+ 3)+ 2= 2x+ 5$ and $w(g(f(x)))= (2x+ 5)^2+ 3= 4x^2+ 20x+ 28$.

Evaluating that at x= 2 gives 4(4)+ 20(2)+ 28= 16+ 40+ 28= 84.

Thanks for your time on here! :-)

-QuantumPixel