Question

Need to calculate: The value of F(3) for the function F(x)=begin{cases}2x if x<3 -5x if xgeq 3 end{cases}

Piecewise-Defined Functions
ANSWERED
asked 2021-02-19

Need to calculate: The value of F(3) for the function \(F(x)=\begin{cases}2x\ if\ x<3 \\-5x\ if\ x\geq 3 \end{cases}\)

Expert Answers (1)

2021-02-20

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,
\(F(x)=\begin{cases}2x\ if\ x<3 \\-5x\ if\ x\geq 3 \end{cases}\)
The function provided is defined in multiple equations.
Therefore, to determine F(3) identify in which equation 3 will lie.
3 lies in the interval \(x \geq 3\). Therefore, to determine the value of F (3), \(F(x) = -5x\) will be used.
Substitute \(x = 3\) into the equation \(F(x) = -5x\).
\(F(x) = -5x\)
\(F(-1) =5*(3)=-15\)
Hence, the value of F(3) is -15.

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