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.

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.