I’m not 100% sure but I think it’s 14/49
79+16, 94+1, 95 +0
Hope this helped !
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 :)
Step-by-step explanation:
if parabola has a vertex not in x-axis, it should have 2 x intercept
x-vertex = -2
first x intercept = 3
second x intercept should -7
so the equation will like this
y = a(x-x1)(x-x2)
y = a (x-3)(x+7)
y = a(x² + 4x - 21)
5 = a((-2)² + 4(-2) - 21)
5 = a(4 - 8 - 21)
5 = a(-25)
a = 5/(-25)
a = -1/5
then the equation is
y = (-1/5)(x² - 4x - 21)
or you can write as
y = -x²/5 + 4x/5 + 21/5
or as this one
5y = -x² + 4x + 21
