Remark
First of all you have to declare the meaning of g(f(x)) After you have done that, you have to make the correct substitution.
Givens
f(x) = 4x^2 + x + 1
g(x) = x^2 - 2
Discussion
What the given condition g(f(x)) means is that you begin with g(x). Write down g(x) = x^2 - 2
Wherever you see an x on either the left or right side of the equation, you put fix)
Then wherever you see f(x) on the right you put in what f(x) is equal to.
Solution
g(x) = x^2 - 2
g(f(x)) = (f(x))^2 - 2
g(f(x)) = [4x^2 + x + 1]^2 - 2
f(x)^2 =
4x^2 + x + 1
<u>4x^2 + x + 1</u>
16x^4 + 4x^3 + 4x^2
4x^3 + x^2 + x
<u> 4x^2 + x + 1</u>
16x^4 + 8x^3 + 9x^2 + 2x + 1
Answer
g(f(x)) = 16x^4 + 8x^3 + 9x^2 + 2x + 1 - 2
g(f(x)) = 16x^4 + 8x^3 + 9x^2 + 2x - 1
Answer:
Coach pug charges $45 only one time, and an additional of $20 per session.
So if you take x sessions, the total cost will be:
c(x) = $45 + $20*x
Dr. Doberman charges only $30 per session, then the cost for x sessions will be_
d(x) = $30*x
Now, which one is better for you?
We need to see the value of x such that:
d(x) = c(x)
$30*x = $45 + $20*x
$30*x - $20*x = $45
$10*x = $45
x = $45/$10 = 4.5
This means that if you take 4 sessions or less, is better the Dr. Doberman, because in this case we do not have an y-intercept.
If you want to have 5 sessions or more, is better Coach Pug, because the slope of the equation is smaller, so the costs for larger values of x will be smaller.
<span>Your answer seems perfectly logical in the world of math. Unfortunately, the world of retail sales calculates markup percentage differently. If a remember correctly, the markup percentage is based upon the final price. Try the following: X is the final selling price. So X minus 70% of X is equal to $66.00 : X-(0.7X)=66, 0.3X=66, 66/0.3=X, X=220
Was $220.00 one possible answer?</span>
Well to simplify it we combine the x's: 4x+11, then to solve for x:
4x= -11
x= -11/4
:)
