Answer:
Hence, g(x) is inverse of f(x)
Step-by-step explanation:
The provided function are f(x)=5x-25 and
To check g(x) is the inverse of f(x)
Plug the formula for g(x) into every instance of "x" in the formula for f (x):
(fog)(x) = f(g(x))
= x+25-25
= x
Now, plug the formula for f (x) into every instance of "x" in the formula for g(x) :
(gof)(x) = g(f(x))
=
=
= x - 5 + 5
= x
Both ways we get "x"
So, both functions are inverse of each other.
Hence, g(x) is inverse of f(x) .
Answer:
Step-by-step explanation:
<u>Equation of a Polynomial</u>
Given the roots x1, x2, and x3 of a cubic polynomial, the equation can be written as:
Where a is the leading coefficient.
We know the three roots of the polynomial -6, -3, and 1, thus:
Since the y-intercept of the polynomial is y=90 when x=0:
90=a(0+6)(0+3)(0-1)
90=a(6)(3)(-1)=-18a
Thus
a = 90/(-18) = -5
The polynomial is:
We must write it in standard form, so we have to multiply all of the factors as follows: