Question

Need to calculate:The value of g(5) from the function g(x)=begin{cases}x-5 if xleq 53x if x>5end{cases}

Piecewise-Defined Functions
ANSWERED
asked 2020-11-06
Need to calculate:The value of g(5) from the function \(g(x)=\begin{cases}x-5\ \ if\ x\leq 5\\3x\ \ if\ x>5\end{cases}\)

Answers (1)

2020-11-07
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,
\(g(x)=\begin{cases}x-5\ \ if\ x\leq 5\\3x\ \ if\ x>5\end{cases}\)
The function provided is defined in multiple equations.
Therefore, to determine g(5) identify in which equation 5 will lie.
5 lies in the interval \(x \leq 5\). Therefore, to determine the value of g(5), \(g(x) = x — 5\) will be used.
Substitute \(x = 0\) into the equation \(g(x) = x — 5\).
\(g(x)=x-5\)
\(g(5)=5-5=0\)
Hence, the value of g (5) is —0.
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