Question

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

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

Answer 1

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.