Sum difference and product of two functions

Question

asked Mar 12, 2019 24.3k views

1 Answer

Dhein · Answer 1 · 2019-03-18T23:55:18+0000

Answer:

1)
(g+h)(x)=4x^2+x+2

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

3)
$(g\bullet h)(-3)=-36$

Explanation:

The given functions are

g(x)=x+2

and

h(x)=4x^2

1)
(g+h)(x)=g(x)+h(x)

This implies that;

(g+h)(x)=x+2+4x^2

Rewrite in standard form to obtain
(g+h)(x)=4x^2+x+2

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

This implies that;

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

Rewrite in standard form to obtain
(g+h)(x)=-4x^2+x+2

3)
$(g\bullet h)(x)=(x+2)(4x^2)$

We now substitute
x=-3 to obtain;

$(g\bullet h)(-3)=(-3+2)(4(-3)^2)$

$(g\bullet h)(-3)=(-1)(36)$

$(g\bullet h)(-3)=-36$