Question

Find when the function f(x) = (2x^2+x-1) / (x^2+x-2) is increasing and decreasing

Answer 1

Ans: f(x) is increasing in interval (-∞,-2)U[-1,1/2]U[2,∞)
f(x) is increasing in interval (-2,-1)U(1/2,1)

Solution:
f(x) can be simplified to

\[f(x)=(x+1)(2x-1)/(x+2)(x-1)\]
now for f(x) to be real, x≠-2,1

Also, f(x) is equal to zero for x=-1,1/2

By wavy curve method, we plot the graph below as follows: