Question 143
The real functions $f(x)=x+1$ and $g(x)=x^{2}+3$ are given.
a) The function $h$ is given by the rule $h(x)=\frac{f(x)+g(x)}{g(x)}$. Compute the stationary points of the function $h$. Write the equation of the horizontal asymptote of the graph of the function $h$ and compute the intersection of the graph with the horizontal asymptote.
b) Compute for which $a \in \mathbb{R}$ the function $j(x)=g(x)+a f(x)-a$ will have at least one real zero.
a) The function $h$ is given by the rule $h(x)=\frac{f(x)+g(x)}{g(x)}$. Compute the stationary points of the function $h$. Write the equation of the horizontal asymptote of the graph of the function $h$ and compute the intersection of the graph with the horizontal asymptote.
b) Compute for which $a \in \mathbb{R}$ the function $j(x)=g(x)+a f(x)-a$ will have at least one real zero.