Chapter 9, Problem 6PFA

To determine

To formulate an expression for $(g-f)(x)$ in standard form.

Answer to Problem 6PFA

  $(g-f)(x)=$ $-2x^2+4x-7$

Explanation of Solution

Given information :

The given functions are:-

  $g(x)=x^2-x-6$ ; $f(x)=3x^2-5x+1$

Formula used :

  $(g-f)(x)=[g(x)]-[f(x)]$

Calculation :

Substituting in the above equation we get,

  $(g-f)(x)=[x^2-x-6]-[3x^2-5x+1]$

Simplifying the expression.

  $=-2x^2+4x-7$

Therefore, $(g-f)(x)=$ $-2x^2+4x-7$ , which is in standard form.