Hi, i need a quick help with my math homework. If it's possible, I would be thankful for more detailed solution, without using matrices, or using graphs only.
1. [MATH]f(x)=\frac{3|x|−3}{|x−1|}[/MATH], [MATH]x \neq 1[/MATH]. Find the set of values of this function.
2. [MATH]f(x)=\frac{2|x|−4}{|x−2|}[/MATH], [MATH]x \neq 2[/MATH]. Find the set of values of this function.
3. [MATH]f(x)=\frac{4−px}{x−p}[/MATH], [MATH]|p| \neq 2[/MATH]. Find all of [MATH]p[/MATH] values, for which the [MATH]f[/MATH] function is increasing in the range [MATH](p,+\infty)[/MATH].
4. [MATH]g(x)=\frac{mx+m+6}{x+m}, m \neq 3, m \neq 2[/MATH]. Find all of [MATH]m[/MATH] values, for which the [MATH]g[/MATH] function in decreasing in the range [MATH](−\infty,−m)[/MATH].
1. [MATH]f(x)=\frac{3|x|−3}{|x−1|}[/MATH], [MATH]x \neq 1[/MATH]. Find the set of values of this function.
2. [MATH]f(x)=\frac{2|x|−4}{|x−2|}[/MATH], [MATH]x \neq 2[/MATH]. Find the set of values of this function.
3. [MATH]f(x)=\frac{4−px}{x−p}[/MATH], [MATH]|p| \neq 2[/MATH]. Find all of [MATH]p[/MATH] values, for which the [MATH]f[/MATH] function is increasing in the range [MATH](p,+\infty)[/MATH].
4. [MATH]g(x)=\frac{mx+m+6}{x+m}, m \neq 3, m \neq 2[/MATH]. Find all of [MATH]m[/MATH] values, for which the [MATH]g[/MATH] function in decreasing in the range [MATH](−\infty,−m)[/MATH].