Let f(x)=root of 1+x² then
a)f(xy) = f(x)f(y)
b)f(xy) >= f(x) f(y)
c)f(xy) <= f(x)f(y)
d)none of these
Answers
Answered by
0
Step-by-step explanation:
f(x)+
f(y)+
2xy−
1
f(x+
y)=
f(x)+
f(y)+
2xy−
1
Put
x=
y=
0
⇒
f(0)=
2f(0)−
1
⇒
f(0)=
1
Now,
f ′
h→0
lim
h
f(x+h)−f(x)
f ′
h→0
lim
h
f(x)+f(h)+2xh−1−f(x)
=
2x+
h→0
lim
h
f(h)−1
=
2x+
f ′
=
2x+
sinϕ
⇒
f ′
2x+
sinϕ
Integrating we get
f(x)=
x 2
xsinϕ+
c
f(0)=
1⇒
1=
c
$$\Rightarrow f(x)=x^2+x \sin \phi +1 ,
f(x)>
0∀x∈
R
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