Question

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If g is the function defined above, then g' is...

Answer 1

Non existent

Answer 2

If g is the function defined by
`g(x)=\left\{\begin{array}{Ir}2-2x, & \text{if } x < 1\\5x-5, & \text{if } x \geq 1\end{array}\right`, then g'(1) is: D. nonexistent.

In Mathematics and Euclidean Geometry, the domain of any piecewise-defined function refers to the union of all of its sub-domains.

Since the value of x is 1, the output value of this piecewise-defined function can be calculated by using the second piecewise-defined function because it is defined over the interval x ≥ 1 as follows;

g(x) = 5x - 5

Next, we would take the first derivative of g(x) as follows;

g'(x) = dy/dx(5x - 5)

g'(x) = 5

In this context, we can logically deduce that g'(1) cannot be determined because it does not exist (non-existent) for an input value of x equals 1;

g'(1) = DNE

Missing information:

`g(x)=\left\{\begin{array}{Ir}2-2x, & \text{if } x < 1\\5x-5, & \text{if } x \geq 1\end{array}\right`

If g is the function defined above, then g'(1) is