• Best of luck to the class of 2019 for their HSC exams. You got this!
    Let us know your thoughts on the HSC exams here
  • Like us on facebook here

VCE Maths questions help (1 Viewer)

boredsatan

Member
Joined
Mar 23, 2017
Messages
565
Gender
Male
HSC
1998
Hi, can I please have some help with the below questions?
f(x) =sqrt(x+1), with a restricted domain of [0, infinity), h(x) = x^2+3, with a domain of R, to find the range of the composite function f(h(x)), the domain would be the domain of the inner function, h(x), which is R, but do we also need to take into account the domain of the outer function, f(x), which is [0, infinity)? Please explain reasoning


g(x) = x^2+4x+4,with a restricted domain of (-infinity, -3], to find the range of the composite function, f(g(x)), the domain of f(g(x)) would be the domain of g(x), which is restricted to (-infinity, -3], but do we also need to take into account the domain of f(x), which is restricted to [0, infinity)? Please explain reasoning


Thanks
 

boredsatan

Member
Joined
Mar 23, 2017
Messages
565
Gender
Male
HSC
1998
y = 18x-6x^3
find the value of x for which y is a maximum and findthe maximum value of y.
i derived the original expression and got 18-18x^2, set it equal to = and got x = -1 and x = 1. How do I know which of these values of x to substitute back into the original expression?
 

InteGrand

Well-Known Member
Joined
Dec 11, 2014
Messages
6,097
Gender
Male
HSC
N/A
y = 18x-6x^3
find the value of x for which y is a maximum and findthe maximum value of y.
i derived the original expression and got 18-18x^2, set it equal to = and got x = -1 and x = 1. How do I know which of these values of x to substitute back into the original expression?
 

boredsatan

Member
Joined
Mar 23, 2017
Messages
565
Gender
Male
HSC
1998
This question is for vce maths methods. The second derivative isn't part of the maths methods course.
Would a gradient sign test work in this instance to find the value of x for maximum and the value of x for minimum?
 

boredsatan

Member
Joined
Mar 23, 2017
Messages
565
Gender
Male
HSC
1998
This question is for vce maths methods. The second derivative isn't part of the maths methods course.
Would a gradient sign test work in this instance to find the value of x for maximum and the value of x for minimum?
bumppppppp
 

boredsatan

Member
Joined
Mar 23, 2017
Messages
565
Gender
Male
HSC
1998
solve 2pi cos(((2pi x - 2pi))/(3) = 0 for 0<x<3

i'd first have to multiply the domain values by the coefficient of x, which is 2pi/3, and would I then need to subtract 2pi/3 form the domain values?

Thanks
 

Users Who Are Viewing This Thread (Users: 0, Guests: 1)

Top