In Exercises 31–50, find f−g and determine the domain for each fu...

Question

In Exercises 31–50, find f−g and determine the domain for each function. f(x) = √x, g(x) = x − 4

Accepted Answer

for the given functions F of X equals the square root of four X. And G F C equals a. S push 12. Find f minus G and write the domain first find f minus G. First. So f minus G. We're gonna do here is we're gonna subtract our two functions. So let's say we take the screw four x. and subtract our other function. Hey next plus 12. I'm gonna put it in parentheses so we make sure they carry over the negative. So we write this we have squared four X -8 X -12. Now we actually have a simplification. We can do here let's take a look at the square four X squared four X from one of our radical roles. We know that we can separate the square root into a product of square roots square the four times the square root of X. Now we can simplify this even further. We notice we have the square before we know what the square the four is. That is just to the square root of X. We just leave because there's nothing, we can simplify there. We just get two squares of X. So if I go back over to our problem, gonna write this as two squares of x -8 X -12. We can write this with the negative eight X. First which is negative X plus two squirts of x minus 12. And I won the final with the domain of this function ist. So the domain is given by any possible restrictions in our function. Let's take a look here if X which doesn't have a restriction Today, the 12 which is a constant which doesn't have a restriction. So let's look at two squirts of X. The square of X does have a restriction. And the square function you can't have a negative number. So if I were to say the square root of negative one, that is not possible and said it's not a real answer. So that doesn't work. Which means the domain of r squared of X function should be zero to infinity because we started zero and we keep going into the positive direction. So this means our overall domain is 0 to infinity. Go ahead and highlight that our equation is negative eight X plus two plus X minus 12, which this corresponds to answer. D. Okay, I hope to help you solve the problem. Thank you for watching. Goodbye.

In Exercises 31–50, find f−g and determine the domain for each function. f(x) = √x, g(x) = x − 4

Key Concepts

Function Operations

Domain of a Function

Composite Functions

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