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The graphs of two linear functions, f(x) and g(x), are shown here on one set of axes:

 

 

Each small box in the grid is 1 unit by 1 unit.  Evaluate f(g(1)) * g(f(1)).

 Dec 14, 2021
 #1
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f(g(1))*g(f(1)) = 3.

 Dec 14, 2021
 #2
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f(x) is a linear equation with slope = -0.5 and y-intercept = 2     --->     f(x)  =  -0.5x + 2

 

g(x) is a linear equation with slope = 1 and y-intercept = 0     --->     g(x)  =  x

 

g(1)  =  1     --->     f( g(1) )  =  -0.5(1) + 2  =  1.5

 

f(1)  =  -0.5(1) + 2  =  1.5     --->     g( f(1) )  =  g(1.5)  =  1.5

 

f( g(1) )  ·  g( f(1) )  = 1.5 · 1.5  =  2.25

 Dec 15, 2021

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