CAT 2003 Slot 1 — QA Question 6

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. (10^y) 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.

Hence, option (b).