A differentiable function satisfy the relation \( \ln (f(x+y))=\ln (f(x)) . \ln (f(y)) \forall x....

Channel:
PW Solutions
Subscribers:
447,000
Published on ● Video Link: https://www.youtube.com/watch?v=6qtO-U_f1W4


Duration: 1:15
1 views
0

A differentiable function satisfy the relation \( \ln (f(x+y))=\ln (f(x)) . \ln (f(y)) \forall x, y \in R, f(0) \neq 1 \),
P
\( f^{\prime}(0)=\mathrm{e} \) and \( g \) be the inverse of \( f \).

The number of solutions of the equation \( \ln [\ln f(x)]=g^{2}[f(x)]-3 g[f(x)]-5 \) is(are) :
(1) 0
(2) 1
(3) 2
(4) Infinite


πŸ“²PW App Link - https://bit.ly/YTAI_PWAP
🌐PW Website - https://www.pw.live



Other Videos By PW Solutions


2024-01-21Let \( f(x) \) be a continuous function such that the area bounded by the curve \( v=f(x) \), th....
2024-01-21The area bounded by \( y=x e^{|x|} \) and lines. \( |x|=1, y=0 \) is W)....
2024-01-21The area of the region bounded by \( 1-y^{2}=|x| \) and \( |x| \) \( +|y|=1 \) is W)....
2024-01-21The area between the curve \( y=2 x^{4}-x^{2} \), the \( x \)-axis and the ordinates of two mini....
2024-01-21The slope of the tangent to a curve \( y=f(x) \) at \( (x, f(x)) \) is \( 2 x+1 \). If the curve....
2024-01-21A differentiable function satisfy the relation \( \ln (f(x+y))=\ln (f(x)) . \ln (f(y)) \forall x....
2024-01-21Let \( f(x)=\min [x+1, \sqrt{(1-x)}] \). Then area bounded by \( f(x) \) and \( x \)-axis is....
2024-01-21Let \( f(x)=\cos ^{-1}\left(2 x^{2}-1\right) \) then....
2024-01-21If \( y=e^{\sqrt{x}} \) then the value of \( \left[4 \cdot y^{\prime}(4)\right] \) (where \( [\c....
2024-01-21If \( f(\theta)=\tan \left(\sin ^{-1} \sqrt{\frac{2}{3+\cos 2 \theta}}\right) \) then :....
2024-01-21A differentiable function satisfy the relation \( \ln (f(x+y))=\ln (f(x)) . \ln (f(y)) \forall x....
2024-01-21\( \frac{d^{2} x}{d y^{2}} \) equals : (1) \( \quad-\left(\frac{d^{2} y}{d x^{2}}\right)^{-1}\le....
2024-01-21If \( y=x \sin x \) then the value of \( y^{i v}(0) \) is....
2024-01-21If \( y=(\sin x)^{\tan x} \), then \( \frac{d y}{d x} \) is equal to :....
2024-01-21The derivative of \( e^{\sin ^{-1}(x)} \) with respect to ' \( \sqrt{1-x^{2}} \), at \( x=1 \) i....
2024-01-21If \( \frac{d y}{d x}=\frac{d}{d x}\left(\frac{\sin ^{4} x+\sin ^{2} x+1}{\sin ^{2} x-\sin x+1}\....
2024-01-21The derivative of an odd function is....
2024-01-21Let \( f(x)=\lim _{n \rightarrow \infty}(\sin x)^{2 n} \), then \( f \) is:....
2024-01-21Let \( f(x)=\left|\begin{array}{ccc}x^{3} & 2 x^{2} & -x \\ 2 x & 1 & 0 \\ x & 0 & 3\end{array}\....
2024-01-21If \( x=e^{t} \cos t \) and \( y=e^{t} \sin t \) then the value of \( \frac{d y}{d x} \) at \( t....
2024-01-21If \( y=\tan ^{-1}\left(\frac{x}{2}\right)+\sin ^{-1}\left(\frac{2}{\sqrt{4+x^{2}}}\right) \) th....