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

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.

x =±sqrt(1/3)

step-by-step explanation:

x+4/6x=1/x

multiply each side by 6x to get rid of the fractions

6x*(x+4/6x)=1/x*6x

distribute

6x^2 +4 = 6

subtract 4 from each side

6x^2 +4-4 = 6-4

6x^2 =2

divide by 6

6x^2/6 = 2/6

x^2 = 1/3

take the square root of each side

sqrt(x^2) = ±sqrt(1/3)

x =±sqrt(1/3)

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answer