Domain of a logarithmic function

Algebra Level 2

$f\left(x\right)=ln\left(x^2+ax+1\right)$ .

The domain of $f(x)$ is $x\in \mathbb{R}$ . $k_1$ and $k_2$ are real numbers so that $k_1<a<k_2$ .

Calculate $k_1+k_2$ .

The answer is 0.

1 solution

Nir S.
Aug 1, 2019

The domain of $f(x)$ is $x\in R$ , therefore $x^2+ax+1>0$ is true for $x\in R$ . That means the trinomial has no zeroes, which means its discriminant is negative: $Δ = a^2 - 4*1*1 < 0 \rightarrow a^2-4<0 \rightarrow -2<a<2$

$k_1=-2 \wedge k_2=2, \rightarrow k_1+k_2=0$ .

Domain of a logarithmic function

The answer is 0.

1 solution

0 pending reports