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

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

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.