Trigonometry help me!!!

Question

f(x)=x g(x)=x-3 h(x)=x^2-9 k(x)=2x

Find each. Show your work.

1. f(g(h(k(2))))
2. f(g(h(k(x))))

Answer 1

For the second problem, f(g(h(k(x)))), you would use the same principle as Denise used.

So starting with the inner most function and working outward.

k(x) = 2x, so plug that into the expression and we get f(g(h(2x))).

Now we evaluate h(2x). h(2x) = (2x)²-9 = 4x²-9

Plug that into the expression and we get f(g(4x²-9))

Now we evaluate g(4x²-9). g(4x²-9) = (4x²-9)-3 = 4x²-12

Plug that into the expression and we get f(4x²-12).

Now we evaluate f(4x²-12) = 4x²-12

So your answer for this problem would be 4x²-12. :)

Answer 2

To get started to begin with the one that is the furthest inside. That would be k(2). We solve this.

k(2) = 2(2) = 4 Since k(2) = 4, we plug that in and get

f(g(h(4)))

So next, we evaluate h(4)

h(4)=4^2-9 = 7, we plug that in to see what the next step is.

f(g(7))

So next, we evaluate g(7)

g(7)=7-3 = 4, we plug that in to see what the last step is

f(4) = 4

So the final answer is 4