A-Level Maths: B8-10 Functions: The Domain of a Composite Function

[AceOfHearts]

Do you have an extension video touching on the range of a composite fumction?

[helenday]

This lesson included some handy tips generally for handling numbers, which I found very helpful, such as the bit where the tutor multiplied both the top and bottom of the fraction by x. Hopefully I will absorb such tips and remember them!

[aunabbas]

you are an amazing teacher. Deliver your lecture very well!!!

[HoneyBee-wrhv]

YOUR A KING, THANKYOU SO MUCH FOR THIS

[kabelan]

hi, i was wondering if you could help with this question. It's given that f(x) = x^2-4, x ∈ ℝ, x>8 and g(x) = 2x-2, x ∈ ℝ, x>3. The question was to determine the domain and range of fg(x). I calculated fg(x) to be 4x^2-8x but i'm still not sure how to work out the domain and range

[larry]

Excellent video, but I'm a bit blurry on a few things. How would you go about drawing the graph of x+2 with the domain not including -2? And why was the domain for gf(x) restricted to -1/2?

[aunabbas]

How to find the domain if the domain of f(x) is restricted lets say 3《 X《7. And they say find the domain of g(x) for which the composite function gf(x) exist?

[AnnaHazel]

If you had three functions (I'm talking hypothetically, so they could be anything - I'll call them f(x), g(x) and h(x)) and you were working out the domain of the composite function fgh(x), would both the domains of g(x) AND h(x) apply?

[TheGamingWattsit]

How do you find the ranges of each composite function

[MathBuz]

For fg(x), if we input value of x = -2
1/(1/(-2+2))
= 1 / (1/0)
= 1 / infinity
= 0
it gives the same answer as we put x = -2 before and after simplification that is zero.
THEN why x = -2 is not included in domain of composite function?

[dansilverman]

What would the domain be of fg(x) if g(x) doesn't have a restricted domain? Thank you

[veem]

Hi there, just a quick question please. Restating your problem, namely:
f(x) = 1/x, where domain is x ∈ ℝ, x ≠ 0 and
g(x) = 1/(x + 2), where domain is x ∈ ℝ, x ≠ -2


What is the domain of fg(x) which = x + 2 ?


Superficially/intuitively, the domain for fg(x) would be x ∈ ℝ ; however, as you say, g(x) comes with “baggage” i.e. x ≠ -2 and hence, you state the domain of fg(x) is therefore { fg(x) : fg(x) x ∈ ℝ, x ≠ -2}.

So, my daft lad question is, why isn’t the domain for fg(x) not the following i.e.
{ fg(x) : fg(x) x ∈ ℝ, x ≠ -2, x ≠ 0 }.


In order words, why isn’t the “baggage” associated with f(x) not included (i.e. f(x) domain is x ∈ ℝ, x ≠ 0) in the domain for fg(x)?


Many thanks for any steer you can provide.

[pandaghee]

For gf(x) how did you get x is not equal to -1/2 I don’t understand when you set the bottom number to zero how could you get -1/2 please explain.