I'm struggling with a question

Question

Madison determined that the function f (x) = 3x +2/4 represents the cost of texting on her current cell phone plan, where 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.

I got 108.05 after my calculations, but I have a feeling that I'm wrong. Can someone give their insight on this?

Answer 1

Mariela, you can find the solution below with detailed algebraic step by step:

Madison knows f(x) = 3x + 2/4 so

When:

x = 36

Then:

f(36) = 3x36 + 2/4

f(36) = 108 + 0.5

f(36) = 108.5

hopefully, it can help.

Answer 2

If f(x) = (3x + 2)/4 you can find the inverse function as follows:

Substitute "y" for "f(x)":

y = (3x + 2)/4

Then swap the places of "x" and "y" to get:

x = (3y + 2)/4

Then solve for "y":

x = (3y + 2)/4

4x = 3y + 2

4x - 2 = 3y

y = (4x - 2)/3

Then replace "y" for f^-1(x)

f^-1(x) = (4x - 2)/3

Plugging in x = 36 we get:

f^-1(36) = (4(36) - 2)/3

f^-1(36) = (144 - 2)/3

f^-1(36) = 142/3 = 47 1/3 texts which, of course would need to be rounded back to 47 texts

An easier way though is to just make f(x) = 36 and solve:

36 = (3x + 2)/4

36(4) = 3x + 2

144 = 3x + 2

142 = 3x

x = 142/3 = 47 1/3 or 47 texts

I'll let you write the complete sentences explaining it.