qr help

[recyrb]

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I have no idea what is going on when given f(x) and g(x) find g(f(x) what does this even mean

just the one example on math destroyer 1, #26 f(x)= Sq root of (x-7) and g(x) = lxl find g(f(x))

The answer is the absolute value of f(x) with absolute value signs insignificant because of the square root.

What is the strategy here, plug what where? completely clueless

Thanks in advance

 

[jhanago]

I have no idea what is going on when given f(x) and g(x) find g(f(x) what does this even mean

just the one example on math destroyer 1, #26 f(x)= Sq root of (x-7) and g(x) = lxl find g(f(x))

The answer is the absolute value of f(x) with absolute value signs insignificant because of the square root.

What is the strategy here, plug what where? completely clueless

Thanks in advance

Okay, so consider the two functions f(x) and g(x). The problems asks you to identify what would happen if you applied one function to the other. In this case. you are taking g(x) of the f(x) function. Essentially, f(x) acts as the "x" in g(x).

What you do is identify what f(x) actually means. since f(x) = sqrt (x-7) then we can say that the value of f(x) = sqrt (x-7) correct?

Now, we apply that to g(f(x)). This is asking you to apply the function to g(x) as if X were = to f(x). Now, you have to think about g(x). What is g(x) the actual equation saying? It says that the value of g(x) = | x |.

Now, since this asks for g(f(x)) instead of g(x) we replace that X with f(x).

So, whatever happens to X in the g(x) equation gets applied to f(x).

Now, we have g(f(x)) = | sqrt (x-7) |

The absolute doesnt matter because the square root of x-7 cant be a negative number anyways, and it has to be positive for sure so absolute value is unnecessary. if that doesnt make sense ill try to rephrase it with respect to your question.