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Answer:
[tex] \displaystyle \boxed{k = 3}[/tex]
Step-by-step explanation:
to determine the Value of k we need to find the equation of f(x) and g(x)
finding the equation of f(x):
f(x) is a linear function which form is given by:
[tex] \displaystyle f(x) =mx + b[/tex]
where:
from the graph we acquire that
[tex]b = 4[/tex]
to figure out m we can consider the following formula:
[tex] \displaystyle m = \frac{ \Delta y}{ \Delta x} [/tex]
from the graph we obtain that both ∆x and ∆y is 1 thus substitute:
[tex] \displaystyle m = \frac{ 1}{ 1} [/tex]
simplify:
[tex] \displaystyle m = 1[/tex]
altogether we acquire:
[tex] \displaystyle f(x) =x + 4[/tex]
finding the equation of g(x):
likewise f(x)
from the graph we obtain that
thus substitute:
[tex] \displaystyle m = \frac{ 3}{ 1} [/tex]
simplify:
[tex] \displaystyle m = 3[/tex]
from the graph we acquire
altogether substitute therefore
[tex] \displaystyle g(x) =3x + 4[/tex]
finding the value of k:
given that,
[tex] \displaystyle \rm f(x) \: \text{and} \: g(x) =f(kx) = 3x + 4[/tex]
so our equation is
[tex] \displaystyle kx + 4 = 3x + 4[/tex]
cancel 4 from both sides:
[tex] \displaystyle kx = 3x [/tex]
divide both sides by x:
[tex] \displaystyle \boxed{k = 3}[/tex]
and we're done!
Disclaimer:
at the following link we posted the complete question
the complete question:
Answer:
k = 3
Step-by-step explanation:
Graph is in attachment .
Finding equation of first line [ f(x) ] :-
We can see that the line passea through point ( 0,4) . Therefore ,
Also it passes through (-4,0 )
Now let's find out slope .So that we can use the slope intercept form to find the equⁿ of the line.
Equation of f(x) :-
Similarly when we will find the equⁿ of g(x) :-
By question :-
