Question

Suppose that the functions g and h are defined for all real numbers x as follows.

Answer 1

Answer:

See below.

Step-by-step explanation:

So we have two functions:

$g(x)=3x-6\\h(x)=5x$

1)

$(g\cdot h)(x)=g(x)\cdot h(x)$

So, substitute and multiply:

$(3x-6)\cdot(5x)\\=5x(3x)-5x(6)\\=15x^2-30x$

2)

Similarly:

$(g+h)(x)=g(x)+h(x)$

Again, substitute and simplify:

$(3x-6)+(5x)\\=8x-6$

3)

To evaluate for -1, find the composition first and then plug in -1. Thus:

$(g-h)(x)=g(x)-h(x)\\(3x-6)-(5x)\\=-2x-6$

Thus:

$(g-h)(x)=-2x-6$

Plug in -1:

$(g-h)(-1)=-2(-1)-6\\=2-6=-4$

Therefore:

$(g-h)(-1)=-4$