You visited us 1 times! Enjoying our articles? Unlock Full Access!

Byju's Answer

Standard XII

Mathematics

Differentiation under Integral Sign

Let f be a gi...

Question

Let f be a given function continuous and derivable for all x and satisfying the relation f(x+y). f(x-y) = f²(x). If f(0) ≠0 find f(x)

Open in App

Solution

Suggest Corrections

Similar questions

If a non-zero function $f$ satisfies the relation $f (x + y) + f (x - y) = 2 f (x) . f (y)$ for all $x, y$ in $R$ and $f (0) \neq 0$ ; then $f (10) - f (- 10) =$

Q. Let

f

be a continuous function satisfying

f (x + y) = f (x) + f (y)

for all

x, y \in R

and

f (1) = 5

then

lim x \to 4 f (x)

is equal to

Q. Let

f (x)

be defined for all

x

ϵ

R

and continuous. Let

f (x + y) - f (x - y) = 4 x y

for all

x, y \in R

and

f (0) = 0

, then

Q. Let

f (x)

be defined for all

x > 0

and be continuous,Let

f (x)

satisfy

f (\frac{x}{y}) = f (x) - f (y)

for all x,y,

f (e) = 1

Then

Q. Let

f

be a non-constant continuous function for all

x \geq 0

. Let

f

satisfy the relation

f (x) = f (a - x) = 1

for some

a ϵ R^{+}

. Then

I = \int_{0}^{a} \frac{d x}{1 + f (x)}

is equal to

Join BYJU'S Learning Program