Find composite functions practice
could someone explain to me in more detail how we go from 2^3√(3x-5)^3+8 to 6x - 2
You are taking the cube root of the expression (3x-5)^3. That means you are finding the expression you need to multiply by itself 3 times to get (3x-5)^3, which is just (3x-5). 2(3x-5) is just 2 times (3x-5). Using distributive property,you would multiply 3x by 2, and -5 by 2, to get (6x-10). Then, -10 +8= -2. So the whole thing simplifies to 6x-2
After you plug in f(x) for the X in h(x), you replace f(x) with the expression equivalent to it. In this case, that would be (3x - 5)^3. Then you have 2 times the cube root of that, and the cube root of an expression cubed would cancel, so now we're left with 2(3x - 5) + 8. then you distribute the 2 and get 6x - 10 + 8, and simplify to get 6x - 2. The answer you gave was the first step, but they asked for the answer to be in terms of X, which means to simplify.
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