Answer:
See below.
Step-by-step explanation:
Composition of the functions is sometimes commutative.
Under certain circumstances, they can be the same. However, most of the time, they are not commutative.
For instance, if we have f(x)=x^2 and g(x)=x^3, then:
Most of the time, however, this won't work.
Edit: Added an example.
The value of k is 3
Solution:
Let us first find the equation of the line f(x).
The points on the line are (-6, -2) and (0, 4).
Here,
Formula to find equation of a line:
Do cross multiplication.
y + 2 = x + 6
y = x + 4
f(x) = x + 4
Given that g(x) = f(kx)
g(x) = kx + 4
The point in the graph of g(x) is ( -2, -2).
g(-2) = k(-2) + 4
we know that g(-2) = -2.
-2 = -2k + 4
Subtract 4 from both sides.
-6 = -2k
Divide by -2 on both sides.
3 = k
k = 3
The value of k is 3.
