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The entire graph of the function f(x) is shown below (f is only defined when x is between -4 and 4 inclusive). How many values of x satisfy f(f(x)) = 2?

Aug 1, 2017
edited by Guest  Aug 1, 2017

#1
+8956
+3

Note that the coordinates are stated this way:  ( x, f(x) )

First, let's find what  x  values cause  f(x)  to equal  2  .

There is the point (-3, 2).     So...     f( -3 )  =  2

There is the point ( 0, 2).     So...     f(  0 )  =  2

There is the point ( 3, 2).     So...     f(  3 )  =  2

Now we want to know what  x  values cause f(x)  to equal  -3, 0, and 3  .

There are no points where f(x) = -3  .

There is the point (-4, 0).     So...     f( -4 )  =  0

There is the point (-2, 3).     So...     f( -2 )  =  3

So...now we know that..

f( f(-4) )             Since  f(-4)  =  0  , we can replace  " f(-4) "  with  " 0 " .

=  f(   0   )              Since  f(0)   =  2  , we can replace  " f(0)  "  with  " 2 " .

=  2

f( f(-2) )             Since  f(-2)  =  3 ,  we can replace  " f(-2) "  with  " 3 ".

=  f(   3   )              Since  f(3)   =  2  , we can replace  " f(3)  "  with  " 2 " .

=  2

There are two  x  values that satisfy  f( f(x) ) = 2  . They are:  x = -4  and  x = -2

Aug 2, 2017
edited by hectictar  Aug 2, 2017

#1
+8956
+3

Note that the coordinates are stated this way:  ( x, f(x) )

First, let's find what  x  values cause  f(x)  to equal  2  .

There is the point (-3, 2).     So...     f( -3 )  =  2

There is the point ( 0, 2).     So...     f(  0 )  =  2

There is the point ( 3, 2).     So...     f(  3 )  =  2

Now we want to know what  x  values cause f(x)  to equal  -3, 0, and 3  .

There are no points where f(x) = -3  .

There is the point (-4, 0).     So...     f( -4 )  =  0

There is the point (-2, 3).     So...     f( -2 )  =  3

So...now we know that..

f( f(-4) )             Since  f(-4)  =  0  , we can replace  " f(-4) "  with  " 0 " .

=  f(   0   )              Since  f(0)   =  2  , we can replace  " f(0)  "  with  " 2 " .

=  2

f( f(-2) )             Since  f(-2)  =  3 ,  we can replace  " f(-2) "  with  " 3 ".

=  f(   3   )              Since  f(3)   =  2  , we can replace  " f(3)  "  with  " 2 " .

=  2

There are two  x  values that satisfy  f( f(x) ) = 2  . They are:  x = -4  and  x = -2

hectictar Aug 2, 2017
edited by hectictar  Aug 2, 2017