sombereki51

2022-09-20

How do you find the domain and range of $y=\frac{-4x-3}{x-2}$?

Guadalupe Reid

Beginner2022-09-21Added 8 answers

The denominator of y cannot be zero as this would make y undefined. Equating the denominator to zero and solving gives the value that x cannot be.

solve $x-2=0\Rightarrow x=2\leftarrow $ excluded value

domain is $x\in \mathbb{R},x\ne 2$

Rearrange the function and make x the subject

$\Rightarrow y(x-2)=-4x-3$

$\Rightarrow xy-2y=-4x-3$

$\Rightarrow xy+4x=2y-3$

$\Rightarrow x(y+4)=2y-3$

$\Rightarrow x=\frac{2y-3}{y+4}$

Again the denominator cannot be zero.

solve $y+4=0\Rightarrow y=-4\leftarrow $ excluded value

range is $y\in \mathbb{R},y\ne -4$

solve $x-2=0\Rightarrow x=2\leftarrow $ excluded value

domain is $x\in \mathbb{R},x\ne 2$

Rearrange the function and make x the subject

$\Rightarrow y(x-2)=-4x-3$

$\Rightarrow xy-2y=-4x-3$

$\Rightarrow xy+4x=2y-3$

$\Rightarrow x(y+4)=2y-3$

$\Rightarrow x=\frac{2y-3}{y+4}$

Again the denominator cannot be zero.

solve $y+4=0\Rightarrow y=-4\leftarrow $ excluded value

range is $y\in \mathbb{R},y\ne -4$

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