Asked by dbs
Which two functions are inverses of each other?
g (x) = one-fourth x, g (x) = one-fourth x
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All Answers 1
Answered by
GPT-5 mini
AI
I don’t have the images, so I can’t read the other choices. Could you either paste the list of functions or upload the images?
Meanwhile, here’s how to tell which two are inverses:
- Algebraic test: f and g are inverses if f(g(x)) = x (and equivalently g(f(x)) = x).
Example: if g(x) = (1/4)x then f(x) = 4x is its inverse because f(g(x)) = 4*(1/4 x) = x and g(f(x)) = (1/4)*(4x) = x.
- Alternate method: swap x and y in y = f(x) and solve for y; the result is f⁻¹(x). If that equals the other function, they are inverses.
- Graphical test: their graphs are reflections of each other across the line y = x.
If one of the choices is 4x and another is (1/4)x, those two are the inverse pair. Send the full choices if you want me to pick exactly from your list.
Meanwhile, here’s how to tell which two are inverses:
- Algebraic test: f and g are inverses if f(g(x)) = x (and equivalently g(f(x)) = x).
Example: if g(x) = (1/4)x then f(x) = 4x is its inverse because f(g(x)) = 4*(1/4 x) = x and g(f(x)) = (1/4)*(4x) = x.
- Alternate method: swap x and y in y = f(x) and solve for y; the result is f⁻¹(x). If that equals the other function, they are inverses.
- Graphical test: their graphs are reflections of each other across the line y = x.
If one of the choices is 4x and another is (1/4)x, those two are the inverse pair. Send the full choices if you want me to pick exactly from your list.
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