Question

The points of discontinuities of the function $fog$ where $g\left(x\right)=\frac{1}{(x-1)}$,$f\left(x\right)=\frac{1}{x^2+x-2}$ are

• A. $\frac{1}{2}$
• B. $2$
• C. $1$
• D. $-2$

Answer 1

Answer: (A), (B), (C)

$2$
$1$
$\frac{1}{2}$

$f\left(x\right)=\frac{1}{x^2+x-2}=\frac{1}{(x+2)(x-1)}$ and $g\left(x\right)=\frac{1}{x-1}$
Then $fog\left(x\right)=\frac{1}{(\frac{1}{x-1}+2)(\frac{1}{x-1}-1)}$
For $x-1\ne 0\Rightarrow x\ne 1$
$fog\left(x\right)=\frac{{(x-1)}^2}{(2x-1)(2-x)}$
And this is defined when
$2x-1\ne 0\Rightarrow x\ne \frac{1}{2}$ and $2-x\ne 0\Rightarrow x\ne 2$
Therefore, point of discontinuity are $1,2,\frac{1}{2}$