Question

Find (f - g)(x) if f(x) = x2 ­- x - 6 and g(x) = 2x2 - 3x + 4

Answer 1

For this question we just have to re-substitute the expressions for their respective functions by assigning them in a plausible condition for two functions. Here, the first function of "x" is subtracted by a second function of "x". The expressions are assigned according to the first and second function expressions in each case or condition.

All we have to do is distribute the parentheses for second expression to deploy positive addition between 2x^2 and 3x. Furthermore grouping all the like terms to get the required answer to this query. So, let me express this via LaTeX interpreter equation editor for a better understanding and clear all the doubts for these forms of queries.

$\mathbf{Since, \: \: f(x) = x^2 - x - 6}$

$\mathbf{\therefore \quad \Big(x^2 - x - 6 - g(x) \Big) \: (x)}$

$\mathbf{Since, \: \: g(x) = 2x^2 - 3x + 4}$

$\mathbf{\therefore \quad x^2 - x - 6 - (2x^2 - 3x + 4)}$

$\mathbf{x^2 - x - 6 - (2x^2) - (- 3x) - (+ 4)}$

$\mathbf{x^2 - x - 6 - 2x^2 + 3x - 4}$

$\mathbf{x^2 - 2x^2 - x + 3x - 6 - 4}$

$\mathbf{x^2 - 2x^2 + 2x - 6 - 4}$

$\mathbf{- x^2 + 2x - 6 - 4}$

$\boxed{\mathbf{\underline{Required \: \: Answer: \: - x^2 + 2x - 10}}}$

Hope it helps.