QJEEAdv07Ma8b86: JEE Advanced 2007 Mathematics - Class 12 JEEAdv07Ma8b86 Solution: If a continuous function defined on the real line , assumes…

Question

Verified Solution • 2025–26 Session moderate

If a continuous function

f

defined on the real line

R

, assumes positive and negative values in

R

then the equation

f(x)=0

has a root in

R

. For example, if it is known that a continuous function

f

on

R

is positive at some point and its minimum value is negative then the equation

f(x)=0

has a root in

R

.
Consider

f\left( x \right) = k{e^x} - x

for all real

x

where

k

is real constant.

For $k>0$ , the set of all values of $k$ for which $k{e^x} - x = 0$ has two distinct roots is

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