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faust18 [17]
2 years ago
10

If f(x) = 2x + 1 and g(x) = -(x - 1)² + 3 what is the smallest solution for f(x)=g(x)?

Mathematics
1 answer:
Sauron [17]2 years ago
5 0

Answer:

<em>The smallest solution is x=-1</em>

Step-by-step explanation:

<em>Quadratic Equation</em>

We have:

f(x)=2x+1

g(x)=-(x-1)^2+3

We'll find the solutions of f(x)=g(x), or:

2x+1=-(x-1)^2+3

Operating:

2x+1=-(x^2-2x+1)+3

2x+1=-x^2+2x-1+3

Rearranging all terms on the left side:

2x+1+x^2-2x+1-3=0

Simplifying:

x^2-1=0

Since the term with the x is missing, we can solve for x:

x^2=1\qquad\Rightarrow x=\sqrt{1}=\pm 1

There are two solutions:

x=1, x=-1

The smallest solution is x=-1

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