Range of a Composite Function

[Peter G.]

Function p and q are defined by:

p (x) = 3x²+1, x∈R, Domain 0≤x≤2
q (x) = x² - 2, x∈R

(q∘p) - State the range:

I got -1 ≤ y ≤ 167

The book says 0 ≤ y ≤ 167

Any idea where I went wrong?

The composite function I got so then I could sub was:
9x⁴ + 6x² - 1

Thanks,
Peter G.

 

[SammyS]

Your answer looks good to me.

Are you sure q(x) is not |x² - 2| ?

 

[Peter G.]

The notation exactly how it is in the book is the following:
q : x → x²-2, x∈R

 

[SammyS]

Looks fine. |x² - 2| was the simplest way I could see to get the book answer, so you appear to be correct: Range = [-1, 167] .

 

[Peter G.]

Cool

Thanks a lot SammyS

And, if you don't mind, what are those two vertical lines?

 

[SammyS]

Absolute value .