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.