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1. Let $f(x)=\left\lfloor\left(-\frac58\right)^x\right\rfloor$ be a function that is defined for all values of $x$ in $[0,\infty)$ such that $f(x)$ is a real number. How many distinct values exist in the range of $f(x)$?

2. The integers $G$ and $H$ are chosen such that $\frac{G}{x+5}+\frac{H}{x^2-4x}=\frac{x^2-2x+10}{x^3+x^2-20x}$ for all real values of $x$ except $-5$, $0$, and $4$. Find $H/G$.

3. Let \[f(x) = \left\{ \begin{array}{cl} ax+3, &\text{ if }x>2, \\ x-5 &\text{ if } -2 \le x \le 2, \\ 2x-b &\text{ if } x <-2. \end{array} \right.\]Find $a+b$ if the piecewise function is continuous (which means that its graph can be drawn without lifting your pencil from the paper).

Guest Apr 24, 2018
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1. Let $f(x)=\left\lfloor\left(-\frac58\right)^x\right\rfloor$ be a function that is defined for all values of $x$ in $[0,\infty)$ such that $f(x)$ is a real number. How many distinct values exist in the range of $f(x)$?

 

2. The integers $G$ and $H$ are chosen such that $\frac{G}{x+5}+\frac{H}{x^2-4x}=\frac{x^2-2x+10}{x^3+x^2-20x}$ for all real values of $x$ except $-5$, $0$, and $4$. Find $H/G$.

3. Let \[f(x) = \left\{ \begin{array}{cl} ax+3, &\text{ if }x>2, \\ x-5 &\text{ if } -2 \le x \le 2, \\ 2x-b &\text{ if } x <-2. \end{array} \right.\]Find $a+b$ if the piecewise function is continuous (which means that its graph can be drawn without lifting your pencil from the paper).

 

laugh

Omi67  Apr 24, 2018
edited by Omi67  Apr 24, 2018

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