Question

For the functions f(x) = 2x^2- 5x + 2 and g(x) = x– 2, find (f/g)(x) and (f/g)(4)

Answer 1

`\left((f)/(g)\right)(x)=(2x^2-5x+2)/(x-2)\\\\\left((f)/(g)\right)(4)=(2\cdot 4^2-5\cdot 4+2)/(4-2)=(32-20+2)/(2)=7`

Answer 2

`(f)/(g)(x)=2x-1\\\\(f)/(g)(4)=7`

Explanation:

`(f)/(g)(x)=(2x^2-5x+2)/(x-2)=((x-2)(2x-1))/((x-2)) =2x-1 \quad\text{x$\\e$2}\\\\(f)/(g)(4)=2\cdot 4-1=7 \qquad\text{fill in 4 for x and do the arithmetic}`