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 :)
Part A you can figure out that the car is traveling at 50 miles an hour because after every hour the distance decreases by 50
b the average change is 100 miles for every 2 hours, which can be simplified back to 50mph which represents the speed of the car
part C {y=-50x+900| (0,900),...(18,0)
Answer:
- The other leg is 82 units
------------------------
Given:
- a = 19,
- c =
, - b = ?
Find the missing leg, using Pythagorean:
- a² + b² = c²
- 19² + b² = 7085
- 361 + b² = 7085
- b² = 7085 - 361
- b² = 6724
- b =
- b = 82
Answer:
3/5+2 does not equal 2/3
Step-by-step explanation:
Hope this helps!
