+753 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?
+9479 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
+9479 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
