Question

Let g(x)=2x and h(x)=x^2+4. evaluate (h o g)(-3)

Answer 1

`\boxed{(h \circ g)(-3) = 40}.`

Explanation:

By the definition of function composition, we have:

`(h \circ g)(-3) = h[g(-3)].`

Since
`g(x) = 2x`, we get:

`g(-3)=2*(-3) = -6.`

On the other hand, since
`h(x) = x^2+4`, we have:

`h[\underbrace{g(-3)}_(=-6)] = h(-6) = (-6)^2 + 4 = 36 + 4 = 40.`

So we finally get:

`\boxed{(h \circ g)(-3) = 40}.`

Answer 2

`g(x)=2x\\\\h(x)=x^2+4\\\\(h\circ g)(x)=(2x)^2+4=4x^2+4\\\\(h\circ g)(-3)\to\text{put x = -3 to the equation of the function}\\\\(h\circ g)(-3)=4(-3)^2+4=4(9)+4=36+4=40\\\\Answer:\ \boxed{(h\circ g)(-3)=40}`