MHB Graphics Coordinate: Is This Correct?

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The discussion confirms that the answer to the graphics coordinate question is E. The inequality (x − 1)⁴ < (x − 1) is satisfied between the x-values of 1 and 2, as demonstrated by evaluating the function at x = 1.5. The intersection of the graphs is found by equating the two functions and factoring the resulting equation. It is noted that the curve y = (x - 1)⁴ lies below the line y = x - 1 exclusively in the interval (1, 2). This analysis affirms the correctness of the initial conclusion regarding the inequality.
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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?
 

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

$$(x-1)^4=x-1$$

$$(x-1)^4-(x-1)=0$$

Now, what do you get when you factor?
 
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.
 
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