Solve the problem.
-For the functionstions $f ( x ) = \sqrt { x ^ { 2 } - 5 x + 6 } \text { and } g ( x ) = \sqrt { x - 2 },$ , fin fid all real values of x where f(x)= g(x).
A)-4, -2
B)2, 4
C)-2, 4
D)no real solution

Question

Quizplus · Accepted Answer

To find the real values of $x$ where $f(x) = g(x)$, we set the two functions equal to each other and solve for $x$:$$\sqrt{x^2 - 5x + 6} = \sqrt{x - 2}$$Squaring both sides to eliminate the square roots gives:$$x^2 - 5x + 6 = x - 2$$Rearranging the equation to set it to 0:$$x^2 - 5x + 6 - x + 2 = 0$$$$x^2 - 6x + 8 = 0$$Factoring or using the quadratic formula, we find the roots of the equation:$$x^2 - 6x + 8 = (x - 4)(x - 2) = 0$$Thus, $x = 4$ or $x = 2$, which are the real values where $f(x) = g(x)$.

Solve the Problem f(x)=x2−5x+6 and g(x)=x−2,f ( x ) = \sqrt { x ^ { 2 } - 5 x + 6 } \text { and } g ( x ) = \sqrt { x - 2 },f(x)=x2−5x+6​ and g(x)=x−2​,

Solve the Problem $f ( x ) = \sqrt { x ^ { 2 } - 5 x + 6 } \text { and } g ( x ) = \sqrt { x - 2 },$