The question regards composite functions. A composite function is a function composed of more than one function. Sorry for saying the word function so many times there, it's just what it is...
The phrase f(g(x)) means 'perform g on an input x, then perform f on the result'. You can then see that there are many options for f(x) and g(x) here, in fact an infinite number of one were to be ridiculous about it.
However a sensible choice might be g(x) = x^2, and f(x) = 2/x + 9. Checking:
g(x) = x^2
f(g(x)) = 2/(x^2) + 9
That is the first question dealt with. Next up is Q2. It is relatively simple to show that these functions are inverses. If you start with a value x, apply a function and then apply the function's inverse, you should return to the same starting value x. To take a common example, within a certain domain, sin^-1(sin(x)) = x.
f(g(x)) = (sqrt(3+x))^2 - 3 = 3 + x - 3 = x
g(f(x)) = sqrt(x^2 - 3 + 3) = sqrt(x^2) = x
A final note is that this is only true for a certain domain, that is x <= 0. This is because y = x^2 is a many-to-one function, so unrestricted it does not have an inverse. Take the example to illustrate this:
If x = -2, f(x) = (-2)^2 - 3 = 4 - 3 = 1
Then g(f(x)) =sqrt(1 + 3) = sqrt(4) = 2 (principal value).
However the question isn't testing knowledge of that.
I hope this helps you :)
Answer:
if she runs more than 8 laps and each lap is 7 minutes she will run more than 56 minutes
she will run 56 minutes t
Answer:
x=482
Step-by-step explanation:
First: x-411=71
Add 411 to both sides, which cancels out the -411 leaving just x.
You add 411 to 71 getting 482.
Answer:
45 minutes
Step-by-step explanation:
It is given that one hose can fill a goldfish pond in 36 minute
So the the first hose can fill goldfish pond 
per minute
When both fill together then they fill in 20 minutes
So the the both hose can fill goldfish pond 
per minute
Let Goldfish pond filled by second hose 
per minute
so 
x=45 minutes
<span>D.The model predicts that for each additional degree that the high temperature is above 70°F, the total number of cones sold increases by 3.7.</span>
