Suppose f(x)=4x-2 and g(x)=2x+1

Question

The answers I've gotten this down to are -2, -3 1/7, 2, and -1 3/11, please tell me which is correct out of all these if any are, and please show the work.

Answer 1

QUESTION:

Which of the answer choices ( -2, -3 1/7, 2, or-1 3/11) could you plug in, to make these two functions equal each other?

ANSWER:

None of the above

WORK:

for x = -2:

f(-2) = 4(-2) - 2 = -10

f(-2) = 2(-2) + 1 = -3

for x = -3 1/7:

f(-3 1/7) = 4(-3 1/7) - 2 = -94/7

g(-3 1/7) = 2(-3 1/7) + 1 = -33/7

for x = 2:

f(2) = 4(2) - 2 = 6

g(2) = 2(2) + 1 = 5

for x = -1 3/11:

f(-1 3/11) = 4(-1 3/11) - 2 = -54/11

g(-1 3/11) = 2(-1 3/11) + 1 = -5/11

REAL QUESTION:

Solve the system of equations (determine the value of x that would yield the same answer for both functions)

f(x) = y_f = 4x - 2

g(x) = y_g = 2x + 1

these linear functions are neither parallel or the same line, therefore, they will intersect at exactly one point. At that point, a single value of x will result in the same y value, in both cases.

if y_f = y_g, then

4x - 2 = 2x + 1

solve for x

4x - 2 + 2 = 2x + 1 + 2

4x - 2x = 2x + 3 - 2x

2x = 3

x = 3/2

CHECK:

f(3/2) = 4(3/2) - 2 = 4

g(3/2) = 2(3/2) + 1 = 4 √

ANSWER:

x = 3/2