smc-4244-70-Square root

Functions and Graphs, SMB-015

State the inequality that defines the domain of the function `g(x) = 2/sqrt(5-x)` ? (2 marks)

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`text(Domain)\ g(x):\ \ x<5`

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`g(x) = 2/sqrt(5-x)\ \ text{exists for:}`

`5-x`	`> 0\ \ \ (5-x!=0)`
`-x`	`> -5`
`x`	`<5`

`:.\ text(Domain)\ g(x):\ \ x<5`

Functions and Graphs, SMB-003

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

--- 5 WORK AREA LINES (style=lined) ---

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

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

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`y = -sqrt(12-x^2)`

`12-x^2>=0\ \ =>\ \ x^2<=12`

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

`y_max =0`

`y_min = -sqrt12\ \ (text{when}\ x=0)`

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

Functions, 2ADV F1 2020 HSC 1 MC

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

`x < 3/2`
`x > 3/2`
`x <= 3/2`
`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 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)

--- 2 WORK AREA LINES (style=lined) ---

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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)` ?

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

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`A`

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`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`