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

User Kilotaras
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1 Answer

1 vote

Answer:

The smallest solution is x=-1

Explanation:

Quadratic Equation

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=√(1)=\pm 1

There are two solutions:

x=1, x=-1

The smallest solution is x=-1

User Lupatus
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