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the function f is defined by f(x) = 2x-2 if x<-1

Ax+B if -1≤x≤1

5x+7 if x>1

Determine the values of A and B if f is continuous on all real numbers (R)

Questioner: angelique

Country: Gauteng, South Africa

Category: Advanced Math

Private: No

Subject: continuity of a function

Question: the function f is defined by f(x) = 2x-2 if x<-1

Ax+B if -1≤x≤1

5x+7 if x>1

Determine the values of A and B if f is continuous on all real numbers (R)

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A piecewise function (that is what you see here) has these features:

1. It has pieces (duhhhh!, or whatever they say in SA.) Each piece has its own RULE.

2. It has breakpoints - the boundary numbers between the pieces.

In this example, the pieces are:

Left: (.. to -1) RULE: 2x-2

Middle: (-1 to 1) Ax+B

Right: (1 to ..) 5x+7

and the breaks at: x = -1, x = 1.

CONTINUITY PRINCIPLE:

The value at a breakpoint must be the same whether you use the rule to the left of the break or the rule to the right of the break.

So f(-1) must be the same whether you use 2x-2 or Ax+B.

and f(1) must be the same whether you use Ax+B or 5x+7.

Does that give you the clue?

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Answers by Expert:

I can answer questions in basic to advanced algebra (theory of equations, complex numbers), precalculus (functions, graphs, exponential, logarithmic, and trigonometric functions and identities), basic probability, and finite mathematics, including mathematical induction. I can also try (but not guarantee) to answer questions on Abstract Algebra -- groups, rings, etc. and Analysis -- sequences, limits, continuity. I won't understand specialized engineering or business jargon.

I taught at a two-year college for 25 years, including all subjects from algebra to third-semester calculus.**Education/Credentials**

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