"Ah! nature keep him warm". ( Narration change )
Answers
Explanation:
Solution−
Given that,
\rm \: f(x) = ln(x) + 3f(x)=ln(x)+3
and
\rm \: g(x) = {e}^{3x}g(x)=e
3x
Now, Consider
\rm \: fog(x)fog(x)
\rm \: = \: f[g(x)]=f[g(x)]
\rm \: = \: f({e}^{3x})=f(e
3x
)
\rm \: = \: ln({e}^{3x}) + 3=ln(e
3x
)+3
We know,
\begin{gathered}\boxed{\tt{ \: \: ln({e}^{x}) = x \: \: }} \\ \end{gathered}
ln(e
x
)=x
So, using this result, we get
\rm \: = \: 3x + 3=3x+3
\rm \: = \: 3(x + 1)=3(x+1)
Hence,
\begin{gathered}\rm\implies \:\rm \: fog(x) = 3(x + 1) \\ \end{gathered}
⟹fog(x)=3(x+1)
Now, Consider
\rm \: gof(x)gof(x)
\rm \: = \: g[f(x)]=g[f(x)]
\rm \: = \: g(lnx + 3)=g(lnx+3)
\rm \: = \: {e}^{3(ln(x) + 3)}=e
3(ln(x)+3)
\rm \: = \: {e}^{3ln(x) + 9}=e
3ln(x)+9
\rm \: = \: {e}^{3ln(x)} \times {e}^{9}=e
3ln(x)
×e
9
We know,
\begin{gathered}\boxed{\tt{ \: y \: ln(x) = ln ({x}^{y}) \: }} \\ \end{gathered}
yln(x)=ln(x
y
)
So, using this, we get
\rm \: = \: {e}^{ln( {x}^{3} )} \times {e}^{9}=e
ln(x
3
)
×e
9
We know
\begin{gathered}\boxed{\tt{ \: {e}^{ln(x)} = x \: }} \\ \end{gathered}
e
ln(x)
=x
So, using this, we get
\begin{gathered}\rm \: = \: {x}^{3} \: {e}^{9} \\ \end{gathered}
=x
3
e
9
Hence,
\begin{gathered}\rm\implies \:\rm \:gof(x) = \: {x}^{3} \: {e}^{9} \\ \end{gathered}
⟹gof(x)=x
3
e
9
Thus,
\begin{gathered}\rm\implies \:\rm \: fog(x) = 3(x + 1) \\ \end{gathered}
⟹fog(x)=3(x+1)
and
\begin{gathered}\rm\implies \:\rm \:gof(x) = \: {x}^{3} \: {e}^{9} \\ \end{gathered}
⟹gof(x)=x
3
e
9
▬▬▬▬▬▬▬▬▬▬▬▬
Answer:
It is being asked to keep him warm.
Explanation:
This is ur answer. Hope it helps... :)