Question

find (fg)(x), where f(x)=2x-5 and g(x)=2-x

Answer 1

Given:

f(x)=2x-5 and g(x)=2-x

To find (fg)(x):

Using the property,

$\begin{gathered} (fg)(x)=f(x)g(x) \\ =(2x-5)(2-x) \\ =4x-2x^2-10+5x \\ =-2x^2+9x-10 \end{gathered}$

Hence, the answer is,

$-2x^2+9x-10$