Composition function rule (f○g)(x) = f(g(x))
<em><u /></em><u>Given the separate functions</u>:

and


This is the distributive property. You take what is outside of the parenthesis and DISTRIBUTE it inside the parenthesis.
- Multiply (-2x-4) by -5:
[(-5)(-2x) + (-5)(-4)] +5x - 4 = -29
= 10x+20+5x-4=-29
- Combine Like Terms:
(10x+5x) + (20-4) = -29
15x+16=-29
- Subtract 16 from each side
15x+16 -16 = -29 -16
15x = -45
x = -3
Given:
Line segment NY has endpoints N(-11, 5) and Y(3,-3).
To find:
The equation of the perpendicular bisector of NY.
Solution:
Midpoint point of NY is




Slope of lines NY is




Product of slopes of two perpendicular lines is -1. So,


The perpendicular bisector of NY passes through (-4,1) with slope
. So, the equation of perpendicular bisector of NY is




Add 1 on both sides.

Therefore, the equation of perpendicular bisector of NY is
.
Given function is

now we need to find the value of k such that function f(x) continuous everywhere.
We know that any function f(x) is continuous at point x=a if left hand limit and right hand limits at the point x=a are equal.
So we just need to find both left and right hand limits then set equal to each other to find the value of k
To find the left hand limit (LHD) we plug x=-4 into 3x+k
so LHD= 3(-4)+k
To find the Right hand limit (RHD) we plug x=-4 into

so RHD= 
Now set both equal





k=-0.47
<u>Hence final answer is -0.47.</u>