Question

Let's Practice!1.Consider the following functions.f(x) = 3x2 + x + 2g(x) = 4x2 + 2(3x – 4)h(x) = 5(x2 - 1)a.lFind f(x) - g(x).b. Find g(x) - h(x).

Answer 1

To find the functions we need to remember that

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

Then

$\begin{gathered} (f-g)(x)=(3x^2+x+2)-(4x^2+2(3x-4)) \\ =3x^2+x+2-(4x^2+6x-8) \\ =3x^2+x+2-4x^2-6x+8 \\ =-x^2-5x+10 \end{gathered}$

Therefore

$f(x)-g(x)=-x^2-5x+10$

Similarly

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

therefore

$g(x)-h(x)=-x^2+6x-3$