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zexius
It's a composite function, which means you need to apply the function to 'g' first, and once you've worked out the result, apply it to 'h'. You work from the inside out.

Therefore, g(t) = 3(t+1), so g(-6) = 3(-6+1)
-6 + 1 is -5, and 3 times -5 is -15. So g(-6) is equal to -15.

Now we apply -15 to the h function, which is h(t) = 2t. So h(-15) = 2(-15). The answer to that is -30.

Hence, your final answer is -30.

There we have an information of two functions [tex] g(t)\, and \, h(t) [/tex]

Using this two functions [tex] g(t)\, and \, h(t) [/tex], we need to find the composition of functions (h\circ g)(t).

The composition of two functions h and g is the new function , by performing g first and then performing h.

[tex] (h\circ g)(t)=h(g(t)) [/tex]

[tex] g(t)=3(t+1) [/tex]

[tex] h(t)=2t [/tex]

Composition of h and g (t) = [tex] (h\circ g)(t) [/tex]

[tex] =h(g(t)) [/tex]

First plugin the value of [tex] g(t)=3(t+1) [/tex]

[tex] h(g(t))=h(3(t+1)) [/tex]

[tex] =h(3t+3) [/tex]

We know that [tex] h(t)=2t [/tex], we need to find h(3t+3),

That is, to replace t by 3t+3,

[tex] =2(3t+3) [/tex]

Now distribute 2 into 3t+3,

[tex] =6t+6 [/tex]

Now plug in [tex] t=-6, [/tex]

[tex] h(g(-6))=6(-6)+6 [/tex]

[tex] =-36+6
\\ =-30 [/tex]

Thus the solution is (D). [tex] h(g(-6))=-30. [/tex]

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