When the curves, y = log10 x and y = x−1 are drawn in the X-Y plane, how many times do they intersect for values of x ≥ 1?
Explanation:
As shown in the above figure, the graphs for, y = 1/x and y = log10 x intersect at only one point.
Hence, option (b).
Alternatively,
To find the point of intersection, we just equate these two functions.
1/x = log10 x
Putting y = 1/x, we get,
10y = 1/y
Here, R.H.S. (i.e. 1/y) cannot be negative as L.H.S. (10y) cannot be negative.
For y = 0, L.H.S. < R.H.S.
for y = 1, L.H.S. > R.H.S.
From this we understand that these two functions intersect each other at least once.
But, 10y is an increasing function and 1/y is a decreasing function.
∴ They intersect each other at a single point only.
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