Domain & Range help for my bestie (1 Viewer)

[NotBamboo]

@Shavi Masee @jane1820
original question:

Find the domain and range for

 

[NotBamboo]

here's my working out (took me forever to write it sooo neatly)

 

[Shavi Masee]

Ty bestiee I probably should have started a new thread when I posted mb T-T

 

[barnyard]

i did the same as you except i used the discriminant being -ive in x^2+2x+3 and then tested x=0 to find that x^2+2x+3 is +ive for all x values ie the domain is all real x
additionally, you can use the parabola's axis of symmetry, -b/2a, instead of using the derivative to find the max y value. taking the inverse will make the lowest y value the highest so the range will be from 0 non inclusive to 1/sqrt2 inclusive (i think that is ext1 graphing and idk if this is an adv question? all the maths gets confused in my head lol)

 

[NotBamboo]

i did the same as you except i used the discriminant being -ive in x^2+2x+3 and then tested x=0 to find that x^2+2x+3 is +ive for all x values ie the domain is all real x
additionally, you can use the parabola's axis of symmetry, -b/2a, instead of using the derivative to find the max y value. taking the inverse will make the lowest y value the highest so the range will be from 0 non inclusive to 1/sqrt2 inclusive (i think that is ext1 graphing and idk if this is an adv question? all the maths gets confused in my head lol)

yes the -b/2a is very helpful
instead of all the messy derivative stuff
i didn't think of it cus it doesn't look like a parabola to me

also what do you mean inverse?

 

[barnyard]

yes the -b/2a is very helpful
instead of all the messy derivative stuff
i didn't think of it cus it doesn't look like a parabola to me

well it was originally a parabola (in fact you even noted this in your working with your u sub) and now it's been transformed a couple times. the sqrt doesnt change anything about WHERE the lowest/highest y value is, just WHAT it is, and the inverse or whatever it is makes the lowest value become the highest and vice versa, leading to y approaching 0 at both x= +ive and -ive infinity

also what do you mean inverse?

1/f(x)
i forgor what it's called feel free to correct me lol

 

[nonya2000]

here's my working out (took me forever to write it sooo neatly)
View attachment 47399

why tf you doing the stupid ass test method? Just sketch a parabola using the zeros after factorising

 

[NotBamboo]

why tf you doing the stupid ass test method? Just sketch a parabola using the zeros after factorising

good luck factorising (x^2 + 2x + 3)
funny answers

 

[Shavi Masee]

good luck factorising (x^2 + 2x + 3)
funny answers

I tried completing the square, that didn't help at all T-T