Porisma

A hint to get started

A parameter hyperbola and a logarithmic input

(i) Sketch the curve with equation y=x+kx+1y=\dfrac{x+k}{x+1}, where k>1k>1.

State the equations of any asymptotes and the coordinates of the points where the curve crosses the axes. marks

(ii) Hence solve the inequality ln⁡x+kln⁡x+1≥0\dfrac{\ln x+k}{\ln x+1}\geq0. marks

[2016/VJC/Promo/10(a)(modified)]

CJC · Review Problems · Question 14

Use y=1+(k−1)/(x+1) to place the two branches before making the log substitution.

Read the worked solution