# VCE Maths questions help (1 Viewer)

#### boredsatan

##### Member
What's the difference between R and R+?

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bumppppppp

#### boredsatan

##### Member
bump, is anyone on this forum?

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#### boredsatan

##### Member
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
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
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?
$\bg_white \noindent Were you given a domain to use? Otherwise, since that's an odd-degree polynomial, it won't have a maximum value on \mathbb{R} (in fact it goes to \infty as x\to-\infty). If you want to find a \emph{local} maximum, you can use the second derivative test.$

#### boredsatan

##### Member
$\bg_white \noindent Were you given a domain to use? Otherwise, since that's an odd-degree polynomial, it won't have a maximum value on \mathbb{R} (in fact it goes to \infty as x\to-\infty). If you want to find a \emph{local} maximum, you can use the second derivative test.$
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
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
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