snowlovelydayM

2020-11-16

Need to calculate:The value of g(0) from the function $g(x)=\{\begin{array}{l}x-5\text{}\text{}if\text{}x\le 5\\ 3x\text{}\text{}if\text{}x5\end{array}$

lobeflepnoumni

Skilled2020-11-17Added 99 answers

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,

$g(x)=\{\begin{array}{l}x-5\text{}\text{}if\text{}x\le 5\\ 3x\text{}\text{}if\text{}x5\end{array}$

The function provided is defined in multiple equations.

Therefore, to determine g(0) identify in which equation 0 will lie.

It lies in the interval$x\le 5$ . Therefore, to determine the value of g(0), $g(x)=x\u20145$ will be used.

Substitute$x=0$ into the equation $g(x)=x\u20145$ .

$g(x)=x-5$

$g(0)=0-5=-5$

Hence, the value of g(0) is —5.

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,

The function provided is defined in multiple equations.

Therefore, to determine g(0) identify in which equation 0 will lie.

It lies in the interval

Substitute

Hence, the value of g(0) is —5.