# Need to calculate:The value of G(0) for the function G(x)=begin{cases}x-5 if x leq -1x if succ 1 end{cases}

Question
Piecewise-Defined Functions
Need to calculate:The value of G(0) for the function $$G(x)=\begin{cases}x-5\ \ if\ x \leq -1\\x\ if\ \succ 1 \end{cases}$$

2021-03-05
Formula used:
Some functions are defined by different equations for various parts for their domains. Those functions are called piecewise-defined functions.
To solve the piecewise-defined function for an input, we will determine that which part of the domain it belongs to and use the appropriate formula for that part of the domain.
Calculation:
Consider the provided function,
$$G(x)=\begin{cases}x-5\ \ if\ x \leq -1\\x\ if\ \succ 1 \end{cases}$$
The function provided is defined in multiple equations.
Therefore, to determine G(0) identifyin which equation 0 will lie.
0 lies in the interval $$x \geq —1$$. Therefore, to determine the value of G(0), $$G(x) = x$$ will be used.
Substitute $$x = 0$$ into the equation.
$$G(x)=x$$
$$G(0)=0$$
Hence, the value of G(0) is 0.

### Relevant Questions

Need to calculate:The value of G(-1) for the function $$G(x)=\begin{cases}x-5\ \ if\ x \leq -1\\x\ if\ \succ 1 \end{cases}$$
Need to calculate:The value of G(-10) for the function $$G(x)=\begin{cases}x-5\ \ if\ x \leq -1\\x\ if\ \succ 1 \end{cases}$$
Need to calculate:The value of g(0) from the function $$g(x)=\begin{cases}x-5\ \ if\ x\leq 5\\3x\ \ if\ x>5\end{cases}$$
Need to calculate: The value of F(-1) for the function $$F(x)=\begin{cases}2x\ if\ x<3 \\-5x\ if\ x\geq 3 \end{cases}$$
Need to calculate:The value of g(6) from the function $$g(x)=\begin{cases}x-5\ \ if\ x\leq 5\\3x\ \ if\ x>5\end{cases}$$
Need to calculate:The value of g(5) from the function $$g(x)=\begin{cases}x-5\ \ if\ x\leq 5\\3x\ \ if\ x>5\end{cases}$$
Need to calculate: The value of F(10) for the function $$F(x)=\begin{cases}2x\ if\ x<3 \\-5x\ if\ x\geq 3 \end{cases}$$
Need to calculate: The value of F(3) for the function $$F(x)=\begin{cases}2x\ if\ x<3 \\-5x\ if\ x\geq 3 \end{cases}$$
Gastroenterology
We present data relating protein concentration to pancreatic function as measured by trypsin secretion among patients with cystic fibrosis.
If we do not want to assume normality for these distributions, then what statistical procedure can be used to compare the three groups?
Perform the test mentioned in Problem 12.42 and report a p-value. How do your results compare with a parametric analysis of the data?
Relationship between protein concentration $$(mg/mL)$$ of duodenal secretions to pancreatic function as measured by trypsin secretion:
$$\left[U/\left(k\ \frac{g}{h}r\right)\right]$$
Tapsin secreton [UGA]
$$\leq\ 50$$
$$\begin{array}{|c|c|}\hline \text{Subject number} & \text{Protetion concentration} \\ \hline 1 & 1.7 \\ \hline 2 & 2.0 \\ \hline 3 & 2.0 \\ \hline 4 & 2.2 \\ \hline 5 & 4.0 \\ \hline 6 & 4.0 \\ \hline 7 & 5.0 \\ \hline 8 & 6.7 \\ \hline 9 & 7.8 \\ \hline \end{array}$$
$$51\ -\ 1000$$
$$\begin{array}{|c|c|}\hline \text{Subject number} & \text{Protetion concentration} \\ \hline 1 & 1.4 \\ \hline 2 & 2.4 \\ \hline 3 & 2.4 \\ \hline 4 & 3.3 \\ \hline 5 & 4.4 \\ \hline 6 & 4.7 \\ \hline 7 & 6.7 \\ \hline 8 & 7.9 \\ \hline 9 & 9.5 \\ \hline 10 & 11.7 \\ \hline \end{array}$$
$$>\ 1000$$
$$\begin{array}{|c|c|}\hline \text{Subject number} & \text{Protetion concentration} \\ \hline 1 & 2.9 \\ \hline 2 & 3.8 \\ \hline 3 & 4.4 \\ \hline 4 & 4.7 \\ \hline 5 & 5.5 \\ \hline 6 & 5.6 \\ \hline 7 & 7.4 \\ \hline 8 & 9.4 \\ \hline 9 & 10.3 \\ \hline \end{array}$$
Consider the function $$\displaystyle{f{{\left({x}\right)}}}={x}^{{{4}}}−{72}{x}^{{{2}}}+{9},-{5}\leq{x}\leq{13}$$.