Question

Lucy found that a solution of x = − 4 was extraneous for her function. What would be a possible denominator in Lucy's function?

x^2 +3x-4
x^2 -9
x+5
x-4

Answer 1

Option 1

Explanation:

We will find the solution for the expression in option 1

`x^2+3x-4`

`x^2+4x-x+4`

`x^2-x+4x-4`

`x(x-1)+4(x-1)`

`(x+4)(x-1)`

Hence, x=1 and x=-4 willl be the solution

Hence,
`x^2+3x-4` will be in denominator.

Hence, Option 1 is correct

Option 2,3 and 4 are discarded.

Answer 2

A solution is extraneous when the denominator of the function becomes zero when the solution is substituted.

Equating each of the options to 0:
x^2 +3x-4 = 0
x = 1 and -4

You can check the other options but they won't result to having a solution of x=-4

Therefore, the possible denominator of the function is x^2 +3x-4