Question

Let f:R------>[1,infinity) be defined as f(x)=log(√3x^2-4x+k+1 +10).If f(x) is surjective then

Answer 1

Root is not over the number 10

Answer 2

@michele_laino

Answer 3

I made conditions for domain and then
I m not getting how shall i proceed

Answer 4

I think that we have to rewrite such conditions, in a more useful way

Answer 5

for example, we can rewrite those conditions as below:
\[\Large \begin{gathered}
{x^2} - \frac{4}{3}x + \frac{{k + 1}}{3} \geqslant 0 \hfill \\
\hfill \\
\left( {\sqrt {{x^2} - \frac{4}{3}x + \frac{{k + 1}}{3}} + \frac{{10}}{{\sqrt 3 }}} \right) > 0 \hfill \\
\end{gathered} \]

Answer 6

from such condiions, I get:
\[\Large \left\{ \begin{gathered}
{\left( {\frac{2}{3}} \right)^2} - \frac{{k + 1}}{3} \leqslant 0 \hfill \\
\hfill \\
{\left( {\frac{2}{3}} \right)^2} - \left( {\frac{{k + 1}}{3} - \frac{{100}}{3}} \right) < 0 \hfill \\
\end{gathered} \right.\]

Answer 7

From your conditions i got k>1/3
And k>301/3 which implies that k>301/3...
Isn't it?