smc-6216-40-Square-Root Functions

Functions, 2ADV F1 2024 HSC 6 MC

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

Show Answers Only

\( D \)

Show Worked Solution

\(x^2-1\)	\(>0\)
\(x^2\)	\(>1\)

\( x<-1 \ \cup \ x>1 \)

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

\( \Rightarrow D \)

What is the domain of `f(x)=1/sqrt{1-x}`?

Show Answers Only

`A`

Show Worked Solution

`text{Cannot have square root of a negative number.}`

`text{Denominator}\ !=0`

`=>A`

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

Show Answers Only

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

Show Worked Solution

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

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

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

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

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

Show Answers Only

`x >= 8`

Show Worked Solution

♦ 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`

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

Show Answers Only

`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`