Question

f(x)=2x^3+6x^2-5x-3g(x)=3x-4Find (f-g)(x).

Answer 1

The functions given in the question are

$f(x)=2x^3+6x^2-5x-3$

While

$g(x)=3x-4$

Find

$(f-g)(x)$

Concept: To evaluate the solution above, we will use the formula below

$(f-g)(x)=f(x)-g(x)$

Step 1: Substitute the values, we will have

$\begin{gathered} (f-g)(x)=f(x)-g(x) \\ (f-g)(x)=2x^3+6x^2-5x-3-(3x-4) \end{gathered}$

Step 2: Expand the brackets and then collect similar terms

$\begin{gathered} (f-g)(x)=2x^3+6x^2-5x-3-(3x-4) \\ (f-g)(x)=2x^3+6x^2-5x-3-3x+4 \\ (f-g)(x)=2x^3+6x^2-5x-3x-3+4 \\ (f-g)(x)=2x^3+6x^2-8x+1 \end{gathered}$

Hence,

(f-g)(x) = 2x³ + 6x² -8x + 1