Question

Perform the indicated operation g(x)=-x-3 h(x) = x 2+X Find (goh) (x)​

Answer 1

Explanation:

h(x) = x^2 + x

g(x^2 + x)

-(x^2 + x) - 3

-x^2 - x - 3

Answer 2

`(g\circ h)(x)=-x^2-x-3`

Explanation:

So we have the two functions:

`g(x)=-x-3\text{ and } h(x)=x^2+x`

And we want to find:

`(g\circ h)(x)`

This is the same thing as:

`=g(h(x))`

So, substitute h(x) into g(x):

`g(x)=-x-3\\g(h(x))=-(x^2+x)-3`

Distribute the negative:

`g(h(x))=-x^2-x-3`

And we're done!

So:

`(g\circ h)(x)=-x^2-x-3`