smc-4244-75-Logarithm

Functions and Graphs, SMB-014

What is the domain of the function `g(x) = log_2(x^2-3)`? (2 marks)

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`text{Domain:}\ x>sqrt3\ \ ∪\ \ x<-sqrt3`

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`g(x)\ text{exists when:}`

`x^2-3`	`> 0`
`x^2`	`> 3`

`x>sqrt3\ \ or\ \ x<-sqrt3`

`:.\ text{Domain:}\ x>sqrt3\ \ ∪\ \ x<-sqrt3`

Functions and Graphs, SMB-013

Factorise the expression `x^2-x-6`. (1 mark)

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What is the domain of the function `f(x) = log_2(x^2-x-6)`? (2 marks)

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i. `x^2-x-6=(x-3)(x+2)`

ii. `text{Domain:}\ x< -2 \ ∪ \ x>3`

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i. `x^2-x-6=(x-3)(x+2)`

ii. `f(x) = log_2(x^2-x-6)=log_2(x-3)(x+2)`

`f(x)\ text{exists when:}`

`(x-3)(x+2)>0`

`x< -2 and x>3`

`text{Domain:}\ x< -2 \ ∪ \ x>3`

Functions and Graphs, SMB-012

What is the domain of the function `f(x) = log_10(3-2x)`? (2 marks)

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`text{Domain:}\ x<3/2`

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`f(x)\ text{exists when:}`

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

Functions and Graphs, SMB-011

What is the domain of the function `g(x) = log_2(x+1)`? (2 marks)

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`text{Domain:}\ x> -1`

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`g(x)\ text{exists when:}`

`x+1`	`> 0`
`x`	`> -1`

Functions and Graphs, SMB-006

State the domain of the function `f(x) = x^2 + log_10(x)`. (2 marks)

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`x>0`

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`f(x) = x^2 + log_10(x)`

`x^2 \ text(is defined for all)\ x`

`log_10 x \ text(is defined for)\ \ x > 0`

`:. \ text(Domain)\ f(x): x>0`

Functions and Graphs, SMB-005 MC

The domain of the function `f (x) = log_2 (2x + 1)` is

`-1/2<x<0`
`text{All}\ x`
`x> -1/2`
`– oo<x<-1/2`

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`C`

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`text(Domain exists for:)`

`2x + 1`	`> 0`
`2x`	`> -1`
`x`	`> -1/2`

`=> C`

Functions and Graphs, SMB-004 MC

What is the domain of the function `f(x) = log_10(4-x)`?

`x < 4`
`x <= 4`
`x > 4`
`x >= 4`

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`A`

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`4-x`	`> 0`
`-x`	`> -4`
`x`	`< 4`

`=> A`