Using the continuity concept, since the lateral limits and the numeric value of the function are equal at the point in which the definition changes, the function is continuous.

<h3>What is the continuity concept?</h3>

A function f(x) is continuous at x = a if it is defined at x = a, and:

$\lim_{x \rightarrow a^-} f(x) = \lim_{x \rightarrow a^+} f(x) = f(a)$

The definition of the piecewise function is given by:

f(x) = 2x - 1, x < 2.

f(x) = 3x/2, x >= 2.

Since the definition of the function changes at x = 2, and the domain of the function has no restrictions, this is the only point in which there may be a discontinuity.

The lateral limits are:

$\lim_{x \rightarrow 2^-} f(x) = \lim_{x \rightarrow 2} 2x - 1 = 2(2) - 1 = 3$ .

$\lim_{x \rightarrow 2^+} f(x) = \lim_{x \rightarrow 2} 1.5x = 1.5(2) = 3$ .

The numeric value is:

f(2) = 1.5 x 2 = 3.

Since the lateral limits and the numeric value of the function are equal at the point in which the definition changes, the function is continuous.

More can be learned about the continuity concept at brainly.com/question/24637240

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4 0

2 years ago

What is the distance from the origin to point A graphed on the complex plane below?

ExtremeBDS [4]

Distance between two points is
Root of X2 - X1 squared + Y2 - Y1 squared
So here X2 is 0 X1 is 0 as the origin is 0,0
Root of Y2-Y1 squared is what we are left with
Root of -2- -3 squared
Root of 1 squared
Root of 1
Which is 1
Distance is 1

5 0

3 years ago

Solve, using the substitution method.

inna [77]

Y - 2x = 8 . . . . (1)
16 + 4x = 2y . . (2)

From (1), y = 2x + 8 . . . (3)

Putting (3) into (2) gives
16 + 4x = 2(2x + 8) = 4x + 16
0 = 0

Therefore, there are infinite number of solutions.

8 0

3 years ago