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Functions, 2ADV F1 2025 HSC 3 MC

What is the domain of the function  \(y=\sqrt{6-x^2}\) ?

  1. \(\left(0, \sqrt{6}\right)\)
  2. \(\left[0, \sqrt{6}\right]\)
  3. \(\left(-\sqrt{6}, \sqrt{6}\right)\)
  4. \(\left[-\sqrt{6}, \sqrt{6}\right]\)
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\(D\)

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\(6-x^2 \geq 6\ \ \Rightarrow\ \ x^2 \leq 6\)

\(-\sqrt{6} \leq x \leq \sqrt{6} \)

\(\Rightarrow D\)

Functions, 2ADV F1 2024 HSC 6 MC

What is the domain of the function  \(f(x)=\dfrac{1}{\sqrt{x^2-1}}\) ?

  1. \([-1,1]\)
  2. \((-\infty,-1] \cup[1, \infty)\)
  3. \((-1,1)\)
  4. \((-\infty,-1) \cup(1, \infty)\)
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\( D \)

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\(x^2-1\) \(>0\)  
\(x^2\) \(>1\)  

 
\( x<-1 \ \cup \ x>1 \)

\( x \in(-\infty,-1) \cup(1, \infty) \)

\( \Rightarrow D \)

Functions, 2ADV F1 2020 HSC 1 MC

Which inequality gives the domain of  `y = sqrt(2x-3)`?

  1. `x < 3/2`
  2. `x > 3/2`
  3. `x <= 3/2`
  4. `x >= 3/2`
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`D`

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`text(Domain exists when:)`

`2x-3` `>= 0`
`2x` `>= 3`
`x` `>= 3/2`

  
`=>D`

Functions, 2ADV F1 SM-Bank 33

  1.  State the domain and range of  `y = -sqrt(12-x^2)`.   (2 marks)

  2.  Sketch the graph.  (1 mark)

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i.  `text(Domain:)\ -sqrt12<=x<= sqrt12`

`text(Range:)\ -sqrt12<=y<= 0`

ii.   

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i.   `y = -sqrt(12-x^2)`

`text(Domain:)\ -sqrt12<=x<= sqrt12`

`text(Range:)\ -sqrt12<=y<= 0`
 

ii.  

Functions, 2ADV F1 2017 HSC 11h

Find the domain of the function  `f(x) = sqrt (3-x)`.  (2 marks)

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`x <= 3 or (-oo,3].`

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`text(Domain of)\ \ f(x) = sqrt (3-x)`

`3-x` `>= 0`
`x` `<= 3`

 

`text(Note domain can also be expressed as:)\ \ (-oo,3]`

Functions, 2ADV F1 2010 HSC 1g

Let  `f(x) = sqrt(x-8)`.  What is the domain of  `f(x)`?   (1 mark)

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 `x >= 8`

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♦ Mean mark 49%.
MARKER’S COMMENT: `x>8` was a common incorrect answer.

`f(x) = sqrt(x-8)`

`text(Domain exists for:)`

`(x-8)` `>= 0`
`x` `>= 8`

Functions, 2ADV F1 2013 HSC 3 MC

Which inequality defines the domain of the function  `f(x) = 1/sqrt(x+3)` ?

  1. `x > -3`  
  2. `x >= -3`  
  3. `x < -3`  
  4. `x <= -3` 
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`A`

Show Worked Solution

`text(Given)\ f(x) = 1/sqrt(x+3)`

`(x + 3)` `> 0`
`x` `> -3`

 

`:.\ text(The domain of)\ f(x)\ text(is)\ \ \ f(x)> -3`

`=>  A`