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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Show Answers Only

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

ii. `text{Domain:}\ x< -2 \ ∪ \ x>3`

Show Worked Solution

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`