Question

Juliana has created the function f(x) =the quantity of 3x plus 2, divided by 4 to represent the cost of texting on her current plan, where x represents the number of texts. Juliana discovers that, using the inverse function to solve for x = 24, she can predict how many texts she can use for $24. Explain to Juliana how to accomplish this, using complete sentences.

Answer 1

Answer:

First, Juliana should write the function as an equation that equates to f(x). She can do this by translating each of the action phrases stated in the question into the form of an expression.

Take the equation f(x) and find its inverse. In the equation, change f(x) to the y variable and switch the x and y variable. Then, isolate y by moving all values to the other side of the equal sign in the backwards order of operations. The y variable should then be changed to f⁻¹(x).

In the inverse function, substitute x for twenty-four and solve. In the final answer, leave in decimal form, rounded down if needed.