- #1

need_aca_help

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## Homework Statement

Question 1:

Which of the following define y as a function of x on R (Real number). Explain for each why they are/ are not function.

a) 4x^3 + y = 6

b) x - y - square root x = 8

c) x = cos^2 y

d) y = (2x + 3) / (x - 1)

Question 2:

Let g(x) = sin(x) and h(x) = 1/x be defined on their natural domains. State the following, giving the domain for each function using set notation.

a) 1 / h(x)

b) (g ∘ h)(x)

c) (h ∘ g)(x)

d) h(x)g(x)

## Homework Equations

None provided.

## The Attempt at a Solution

Question 1

a)

*y = 6 - 4x^3*

Function exists

Function exists

b)

*y = x - square root x - 8*

Function exists if x = R

Function exists if x = R

c)

*?*

d)

*Function exits if x = R*

Function exists R \ {1}

Function exists R \ {1}

Question 2:

a)

*1 / (1/x) = x | x element R*

b)

*g(h(x)) = sin(1/x) | x ≠ infinity*

c)

*h(g(x)) = 1 / sin(x) | x ≠ 0*

d)

*(1/x)(sin(x)) = sin(x) / x | x ≠ 0*

**OP's message:**

I am having trouble understanding how to do these questions and also to write down the reasons in a mathematical way...

I have skipped the working since it will be difficult to type them. I will post a photo if necessary.

Please explain the answer if they are wrong...