If is the curve obtained by reflecting in the line

MATHEMATICS · Single correct · A Level · Mathematics · Algebra and Functions · Algebra and Functions

Problem

g(x)

is the curve obtained by reflecting

f(x)=\frac{e^x-e^{-x}}{2}

in the line

y=x

, then (1)

g(x)

has more than one tangent parallel to the

x

-axis. (2)

g(x)

has more than one tangent parallel to the

y

-axis. (3)

y=-x

is a tangent to

g(x)

(0,0)

. (4)

g(x)

has no extremum.