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
asked 2021-03-04
Need to calculate:The value of G(0) for the function \(G(x)=\begin{cases}x-5\ \ if\ x \leq -1\\x\ if\ \succ 1 \end{cases}\)

Answers (1)

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.
0

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...