Solving Equations and Functions

The video tutorial explains how to solve the equation f(x) = 3/x - 4/(3x) for f(x) = -7. It involves substituting -7 into the function, clearing fractions by multiplying by the least common denominator, and solving for x. The solution is verified graphically by finding the intersection point of the function and the line y = -7.

What is the initial function given in the problem?

• f(x) = 3/x - 4/3x

• f(x) = 3x + 4/3x

• f(x) = 3/x + 4/3x

• f(x) = 3x - 4/3x

What value are we trying to find for f(x)?

• 0

• -7

• -5/21

• 7

What is the equation formed after substituting -7 for f(x)?

• -7 = 3x - 4/3x

• -7 = 3x + 4/3x

• -7 = 3/x + 4/3x

• -7 = 3/x - 4/3x

What is the least common denominator used to clear the fractions?

• 3x

• 3

• 9x

• x

What is the result of multiplying 3x by -7?

• -21x

• 7x

• -7x

• 21x

What is the simplified form of 3x times 3/x?

• 1

• 0

• 9

• 3

What is the value of x that solves the equation?

• -7

• -5/21

• 7

• 5/21

How is the solution verified graphically?

• By checking the slope of the line

• By finding the intersection point

• By calculating the area under the curve

• By comparing with another function

What is the ordered pair of the intersection point?

• (5/21, 7)

• (-5/21, -7)

• (-5/21, 0)

• (0, -7)

What does the intersection point indicate about the function?

• The function has no solution

• The function is linear

• The input and output match the solution

• The function is undefined