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:
x=4
Step-by-step explanation:
5-3(2x-7)=5-6x+21=-6x+26
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12-5(x-2)=12-5x+10=-5x+22
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-6x+26=-5x+22
-6x-(-5x)=22-26
-6x+5x=-4
-x=-4
x=4
Answer:
A. <u>Distance of the lightning after 4 seconds = 744,000 miles</u>
<u>B. Distance of the lightning after n seconds = 186,000 * n</u>
Step-by-step explanation:
1. Let's review the information given to us to answer the question correctly:
Speed of lightning = 186,000 miles per second
Speed of sound = 750 miles per hour
2. A. If you see a flash of lightning, then hear the thunder 4 seconds later, how far away is the lightning?
Distance of the lightning after 4 seconds = 186,000 * 4
<u>Distance of the lightning after 4 seconds = 744,000 miles</u>
<u>B. Now let’s generalize that result. Suppose it takes n seconds to hear the thunder after a flash of lightning. How far away is the lightning, in terms of n?</u>
<u>Distance of the lightning after n seconds = 186,000 * n</u>
Answer:
The rate is $18.15 per mile.
Step-by-step explanation:
Add $18 + $0.15 and it equals $18.15.
