How to find the graph g(-f(x))?

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Can someone please explain to me how to do question 23? Thanks!

1 Answer
Apr 5, 2018

Graph B

Explanation:

Notice that the range (the output) of #f(x)# is never positive #([-infty#,#0])# for any value of #x# (the input). This means that the range (the output) of #-f(x)# is never negative #([0#,#infty])# for any value of #x# (the input). (The negative sign in front of #f(x)# means that the graph of the #f(x)# is flipped with respect to the x-axis.)

Also, notice that when #x# (the input) is positive, the range (the output) of #g(x)# is positive.

Since the range (the output) of #-f(x)# is never negative, the range (the output) of #g(-f(x))# is never negative. (The output from #-f(x)# becomes the input to #g(x)#.)

Therefore, the correct graph is: Graph B.