The best approximated value of g(h(1)) is -5 and this can be determined by using the given graph.
Given :
Graph of the function f(x) and g(x).
The following steps can be used in order to determine the approximate value of g(h(1)):
Step 1 - The function (y = g(x)) represents the straight line passing through (-2.5,0) and (0,-5).
Step 2 - The equation of a line passing through (-2.5,0) and (0,-5) is given below:
![\dfrac{y -0}{x+2.5}=\dfrac{-5-0}{0+2.5}](/tpl/images/0773/0046/df8da.png)
y = -2(x + 2.5)
y = -2x - 5
Step 3 - According to the graph, the value of the function 'h' at (x = 1) is 0.
Step 4 - Now, the value of g(h(1)) can be calculated as:
![\rm g(h(1)) = -2(0)-5](/tpl/images/0773/0046/edb8d.png)
g(h(1)) = -5
Therefore, the correct option is B).
For more information, refer to the link given below:
link