Question

g(x) = 4x – 2h(x)= x^2 - 5xFind g(x) – h(x)

Answer 1

We have the functions:

$\begin{gathered} g\mleft(x\mright)=4x-2 \\ h\mleft(x\mright)=x^2-5x \end{gathered}$

And we are asked for:

$g\mleft(x\mright)-h\mleft(x\mright)$

Which is to subtract the function h(x) from the function g(x).

The result of this subtraction is as follows:

$g\mleft(x\mright)-h\mleft(x\mright)=4x-2-(x^2-5x)$

First, we multiply the minus sign outside the parenthesis by the numbers inside it:

$g(x)-h(x)=4x-2-x^2+5x$

Now, we leave the term with the greatest exponent at the beginning and we add the like terms 4x and 5x which result in 9x.

So the simplified expression is as follows:

$g\mleft(x\mright)-h\mleft(x\mright)=-x^2+9x-2$

Answer:

$g(x)-h(x)=-x^2+9x-2$