The composite function
works like this:
- Take a number
as input - Evaluate h(x) = 3x. Let's call this output z.
- Evaluate g(x) = 1/(z+2)
So, if we substitute back z = 3x, the final output is 1/(3x+2). We know that the denominator of a fraction can't be zero, so we must impose
![3x+2 \neq 0 \iff 3x \neq -2 \iff x \neq -\dfrac{2}{3}](https://tex.z-dn.net/?f=%203x%2B2%20%5Cneq%200%20%5Ciff%203x%20%5Cneq%20-2%20%5Ciff%20x%20%5Cneq%20-%5Cdfrac%7B2%7D%7B3%7D%20)
![\bf \cfrac{x^2+6x-9}{x-2}\qquad \begin{cases} x^2\impliedby \textit{has a degree of 2}\\ x^1\impliedby \textit{has a degree of 1} \end{cases}](https://tex.z-dn.net/?f=%5Cbf%20%5Ccfrac%7Bx%5E2%2B6x-9%7D%7Bx-2%7D%5Cqquad%20%0A%5Cbegin%7Bcases%7D%0Ax%5E2%5Cimpliedby%20%5Ctextit%7Bhas%20a%20degree%20of%202%7D%5C%5C%0Ax%5E1%5Cimpliedby%20%5Ctextit%7Bhas%20a%20degree%20of%201%7D%0A%5Cend%7Bcases%7D)
if the degree of the expression of the numerator is greater than that of the denominator, the rational expression has no horizontal asymptote.
Answer:
2. 3/4 x 5/9 = 3x5/4x9 = 15/36 = 5/12
4. 4/7 x 1/2 = 4x1/7x2 = 4/14 = 2/7
6. 4/9 x 2/3 = 4x2/9x3=8/27
Step-by-step explanation:
Hope it helps!
Answer:
<h2>m
![\angle](https://tex.z-dn.net/?f=%5Cangle)
F = 34°</h2>
Step-by-step explanation:
If E and F are complementary I means that the sum of their angles add up to 90° since all complementary angles have the sum of their angles equal to 90°
To find m
F add m
E and m
F and equate it to 90 to find x then substitute it into the expression for m
F
Thats
m
E + m
F = 90
9x - 38 + 2x + 40 = 90
11x + 2 = 90
11x = 90 - 2
11x = 88
Divide both sides by 11
x = 8
Now we have
if m
F = 9x - 38
m
F = 9( 8) - 38
m
F = 72 - 38
We have the final answer as
<h3>m
![\angle](https://tex.z-dn.net/?f=%5Cangle)
F = 34°</h3>
Hope this helps you