Question

Let f(x) = 2x^4 -3x^2 and g(x) = 6x^2 -5x+2What is the rule for ( f - g ) (x)?

Answer 1

ANSWER

(f - g)(x) = 2x⁴ - 9x² + 5x - 2

EXPLANATION

To subtract two functions:

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

We have to replace each function with its expression:

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

And add like terms:

$\begin{gathered} f(x)-g(x)=2x^4-3x^2-6x^2+5x-2 \\ f(x)-g(x)=2x^4-9x^2+5x-2 \end{gathered}$