Graphics Coordinate: Is This Correct?

[squexy]

View attachment 2983

The answer is E.

Since the line is passing the parable at x = 1 and 2 I used between these values to satisfy the inequality(x − 1)4< (x − 1)X = 1,5

(1,5 -1)4 < (1,5 -1)
0,0625 < 0,5

Is this correct?

 

[MarkFL]

I would begin by finding the $x$-values for which the two graphs intersect. We can do this by equating the two functions:

\(\displaystyle (x-1)^4=x-1\)

\(\displaystyle (x-1)^4-(x-1)=0\)

Now, what do you get when you factor?

 

[Dethrone]

I was going to type exactly what MarkFL did, but he beat me at it :p

I also want to note that the question has graciously graphed the curves for us, and by inspection, we see that $y=(x-1)^4$ is under the line $y=x-1$ on the interval $(1, 2)$ only, which is the only interval that satisfies your inequality.