In this question you must show detailed reasoning.

The function $f\,$ is defined by $f(x)=x+1(x−1)(x−2)\displaystyle f(x)=\frac{x+1}{(x-1)(x-2)}$ , where $x\ne1\,$ and $x≠2x\ne2$ .

Express $f (x)$ in partial fractions.

Show that, for a constant $k$ , the equation $f (x) = k$ can be written as $kx^2-(3k+1)x+2k-1=0$ .

Determine the values of $k\,$ for which the equation $f (x) = k$ has exactly one real solution.

In this question you must show detailed reasoning.

The function $f\,$ is defined by $f(x)=x+1(x−1)(x−2)\displaystyle f(x)=\frac{x+1}{(x-1)(x-2)}$ , where $x\ne1\,$ and $x≠2x\ne2$ .

Express $f (x)$ in partial fractions.

Show that, for a constant $k$ , the equation $f (x) = k$ can be written as $kx^2-(3k+1)x+2k-1=0$ .

Determine the values of $k\,$ for which the equation $f (x) = k$ has exactly one real solution.

1 Pure Mathematics

1 Pure Mathematics Questions