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  • 21-01-2022
  • Mathematics
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Using the three steps, determine the value of A such that f(x) is continuous everywhere.

f(x) = x - 3 x < 2
-1 x = 2
x^2 + Ax-5 x > 2

Using the three steps determine the value of A such that fx is continuous everywhere fx x 3 x lt 2 1 x 2 x2 Ax5 x gt 2 class=

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Algebraic122 Algebraic122
  • 21-01-2022

Answer:

a=0

Step-by-step explanation:

When x=2, it is at -1, so the left and right side of x=2 must approach -1, in order for it to be defined, and must be undefined at x=1 to be continuous.

We plug in 2 in the bottom equation and set it equal to -1.

[tex]( {2}^{2} + a(2) - 5 = - 1[/tex]

[tex]4 + 2a - 5 = - 1[/tex]

[tex]2a = 0[/tex]

[tex]a = 0[/tex]

So

A=0

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