Answer: Choice B. k(h(g(f(x))))
For choice B, the functions are k, h, g, f going from left to right.
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Explanation:
We have 4x involved, so we'll need f(x)
This 4x term is inside a cubic, so we'll need g(x) as well.
So far we have
g(x) = x^3
g( f(x) ) = ( f(x) )^3
g( f(x) ) = ( 4x )^3
Then note how we are dividing that result by 2. That's the same as applying the h(x) function
[tex]h(x) = \frac{x}{2}\\\\h(g(f(x))) = \frac{g(f(x))}{2}\\\\h(g(f(x))) = \frac{(4x)^3}{2}\\\\[/tex]
And finally, we subtract 1 from this, but that's the same as using k(x)
[tex]k(x) = x-1\\\\k(h(g(f(x)))) = h(g(f(x)))-1\\\\k(h(g(f(x)))) = \frac{(4x)^3}{2}-1\\\\[/tex]
This leads to the answer choice B.
To be honest, this notation is a mess considering how many function compositions are going on. It's very easy to get lost. I recommend carefully stepping through the problem and building it up in the way I've done above, or in a similar fashion. The idea is to start from the inside and work your way out. Keep in mind that PEMDAS plays a role.
