I didn't even notice that. However, I checked, it's the same as I have written it. Probably a mistake.Did you mean
View attachment 32468
I would do the evaluation of f(g(f(g(1/2)))) step by step, rather than trying to write a single expression.
What is g(1/2)? It's -2(1/2) = -1, because 1/2 > 0.
What is f(-1)?
And so on.
Just realized that I was echoing @Dr.Peterson, but at least my typesetting is fancierI would approach this one step at a time:
[math]f \left(\frac{1}{2}\right) = ?[/math][math]g\circ f \left(\frac{1}{2}\right) = ?[/math],
[math]f \circ g\circ f \left(\frac{1}{2}\right) = ?[/math],
[math]g \circ f \circ g\circ f \left(\frac{1}{2}\right) = ?[/math],
Evaluate it as the notation requires. Both of us (mister fancy and I) showed you where to start.I didn't even notice that. However, I checked, it's the same as I have written it. Probably a mistake.
Would you start evaluating from left or right side?
I hadn't noticed until now that @blamocur showed how to answer the wrong question! What he said would be correct if you had wanted [imath]g \circ f \circ g\circ f \left(\frac{1}{2}\right)[/imath]; but you want [imath]f \circ g \circ f\circ g \left(\frac{1}{2}\right)[/imath].Would you start evaluating from left or right side?
I got 0I hadn't noticed until now that @blamocur showed how to answer the wrong question! What he said would be correct if you had wanted [imath]g \circ f \circ g\circ f \left(\frac{1}{2}\right)[/imath]; but you want [imath]f \circ g \circ f\circ g \left(\frac{1}{2}\right)[/imath].
I guess I did not echo you correctly -- thanks for the correction.I hadn't noticed until now that @blamocur showed how to answer the wrong question! What he said would be correct if you had wanted [imath]g \circ f \circ g\circ f \left(\frac{1}{2}\right)[/imath]; but you want [imath]f \circ g \circ f\circ g \left(\frac{1}{2}\right)[/imath].
okay i will keep that in mind!Looks good me.
My only concern is that you never answered the question in my opinion!
You should have somewhere that fogofog(1/2) = 0. In my opinion this is important. I would definitely take off some credit on an exam for failing to state the answer.
Echo sounds real nice in the corner. Trust me I know that from experience.I guess I did not echo you correctly -- thanks for the correction.