Please explain why you wrote f(x)=2x and f(x)+1. (I'm guessing that you are not recognizing that f(x) has a specific meaning in this problem, and are just writing "f(x)" to mean "what I've done so far".) It looks like you're trying to solve a different problem than what you showed.
All you have to do for this problem is to replace x in 2x + 1 with (-x).
Now, it is true that 2x + 1 = 2(x + 0.5); but why would you do that in this problem? That is f(x), not f(-x), and it doesn't help toward the answer.Furthermore, the y-intercept of f(x) = 2x + 1 is 1, regardless of which way you write it.
I am learning the transformation of graph and this question appears in the transformation of the graph. But i don't really understand why x-intercept is 0.5 and -0.5 after the transformation of 2x+1. Please help!
Yes the line f(x) =2x+1 was reflected in the y-axis.
The x-intercept of f(x)=2x+1 is found by substituting y=0.
The x-intercept of f(-x) can be found in one of 2 ways:
1. f(-x) = 2(-x)+1 = -2x+1 and substitute y=0 to find x-int is 1/2
2. Recognise that f(-x) is a reflection of f(x) in the y-axis, so the original x-int of -1/2 gets reflectd onto the x-int of 1/2.