BRAINLEST! Madison determined that the function f(x)=3x+24 represents the cost of texting on her current cell phone plan, where x represents the number of texts. She discovers that using the inverse function to solve for x = 36, she can predict the how many texts she can use for $36. Explain to Madison how to accomplish this, using complete sentences. You may show any algebraic work necessary to support your explanation.

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altavistard altavistard · Answer 1 · 2021-05-02T14:40:19+02:00

Answer:

Step-by-step explanation:

Start with f(x)=3x+24 and find the inverse function:

1. Replace "f(x)" with y: y = 3x + 24

2. Interchange x and y: x = 3y + 24

3. Solve for y: 3y = x - 24, or y = (1/3)(x - 24)

This last step results in the inverse function.

Now let's test this. Let x = 36. How many texts could Madison "do" for this dollar amount? y = (1/3)(36 - 24) results in y = (1/3)(12), or 4 (texts).

Let's go back to the original f(x)=3x+24, now letting x = 4:

f(x)=3(12)+24 = $36. This verifies that y = (1/3)(x - 24) is the inverse function of f(x) = 3x + 24.