Question

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

Answer 1

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