Given functions f and g, (b)

Question

(g \circ ƒ) (x)

and its domain. See Examples 6 and 7.

$ƒ (x) = - 6 x + 9, g (x) = 5 x + 7$

Accepted Answer

Hello, everyone. We've been asked to determine G of F of X for the functions F of X equals negative three X plus 22 G of X equals to X plus 13, we also need to find the domain of G of F of X. I'm going to rewrite this with parentheses. So I'm going to write it is G and then open parentheses. And I'm putting F of X in there. I do this because it helps me see that I'm putting the F of X function into the G function. So I'm going to replace the letters F of X with the actual F of X function. So now I have G of negative three X plus 22. So I know I'm putting negative three X plus 22 in for X in the G function. So that should look like two times negative three X plus 22 And then plus 13. So I'm gonna distribute the two into the parentheses, two times negative three, X gives me negative six X, two times 22 is 44. Still plus 13. Combining my like terms. I still have a negative six X plus 57 when I add 44 13. So this looks like my G of F of X function is gonna be negative six X plus 57. So this is part of our solution. We're not quite done yet as we are asked to find the domain also. So now that we know G of F of X, we can look for its domain. Recall that the domain is all the X values that will make the function come out to a real number. Always check our special cases. If we have a square root or any sort of radical, we don't. In this case, if we have a fraction, make sure it's not undefined. No fractions, all positive and negative numbers should work there. Which means our domain is all real numbers. So it goes from negative infinity to positive infinity. So G of F of X equals negative six X plus with the domain of all real numbers. And that's answer choice C have a nice day.

Given functions f and g, (b) $(g \circ ƒ) (x)$ and its domain. See Examples 6 and 7.
$ƒ (x) = - 6 x + 9, g (x) = 5 x + 7$

Key Concepts

Function Composition

Domain of a Composite Function

Linear Functions and Their Domains

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