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Given f(x) and g(x)= f(k•x), use the graph to determine the value of k

Sagot :

Nayefx

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:

  • m is the slope
  • b is the y-intercept

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

  • ∆x=1
  • ∆y=3

thus substitute:

[tex] \displaystyle m = \frac{ 3}{ 1} [/tex]

simplify:

[tex] \displaystyle m = 3[/tex]

from the graph we acquire

  • b=4

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:

  • https://brainly.com/question/24201282
VirαtKσhli

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 ,

  • y intercept = 4

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.

  • m = y ₂ - y₁ / x ₂ - x₁
  • m = 4 - 0 / 0 - (-4)
  • m = 4/4
  • m = 1

Equation of f(x) :-

  • y = mx + c
  • y = 1 * x + 4
  • y = x + 4
  • f(x) = x + 4

Similarly when we will find the equⁿ of g(x) :-

  • y = 3x + 4
  • g(x) = 3x + 4

By question :-

  • f(x ) and g(x) = f ( k • x )
  • 3x + 4 = kx + 4
  • kx = 3x
  • k = 3
View image VirαtKσhli
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