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

Answer:

The smallest solution is x=-1

Step-by-step 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:

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

There are two solutions:

x=1, x=-1

The smallest solution is x=-1