Given functions f and g, find (a)

Question

(ƒ \circ g) (x)

and its domain. See Examples 6 and 7.

$ƒ (x) = x^{3}, g (x) = x^{2} + 3 x - 1$

Accepted Answer

Hello, everyone. We've been asked to determine F of G of X for the functions F of X equals X to the third and G of X equals to X squared minus eight X plus nine. We also need to find the domain of F of G of X. I'm going to rewrite F of G of X using some parentheses so I can rewrite as F of and then G of X is inside those parentheses. I do this because it's a little clearer to me to see what gets plugged in where. So now I know that I want to put the G of X function into the F function. So I know it's F of two X squared - x plus nine. So now writing it that way, I can see that I am plugging two X squared minus eight X plus nine into the F function for X. And when I do that, I get to X squared minus eight X plus nine to the third power. Now, here's where checking your answer choices comes in handy before you multiply that all out look over, none of them are expanded. This will be our function So this is our F of G of X. It is in parentheses, two X squared minus eight X plus nine, all of it to the third power. So we're not quite done as we need to find the domain still. But I am happy that I did not need to multiply that try no meal three times. So our domain recall that a domain is all the values that give us a real number as a solution to our function. So if I plug a negative number into this function, will I get a real number? Yes, but plug a positive in while I get a real number? Yes. Are there any radicals or fractions that I have to worry about? No. So my domain is all real numbers which we write as negative infinity to positive infinity. So this is our full solution that F of G of X equals two X squared minus eight X plus nine, all of it to the third power with the domain of all real numbers. And that is answer choice B have a nice day.

Given functions f and g, find (a) $(ƒ \circ g) (x)$ and its domain. See Examples 6 and 7.
$ƒ (x) = x^{3}, g (x) = x^{2} + 3 x - 1$

Key Concepts

Function Composition

Polynomial Functions

Domain of Composite Functions

Watch next