Grades 11-12 Video Solutions 2013-Levels 11&12 Video Solutions 2013 problem17

Levels 11&12 Video Solutions 2013 problem17

Video Transcription

Video Summary

The video discusses finding the number of solutions to the equation \( f(f(f(x))) = 0 \) for a piecewise function composed of two rays and a line segment. It details the equations of the function's components: two lines \( y = x + 4 \) and \( y = -x \). By evaluating \( f(f(x)) = -4 \) or \( 0 \) for these lines, the solutions are determined. The possible values for \( x \) are worked out as \( 0, -4, -8, \) and \( -12 \). Thus, there are four solutions to the equation, and the answer is option A.

Keywords

piecewise function

equation solutions

rays and line segment

nested function

mathematical analysis