Question

Which function represents the inverse of function f?

Answer 1

Answer: Choice [B]

Explanation:

Hii, I'd love to help you out! (:

This particular problem is all about finding inverse functions.

This can be done in 3 easy steps, which are shown below.

1. Replace f(x) with y
2. Switch x and y places
3. Solve for y

The process is shown below.

`\multimap\quad \tt f(x)=3x+5 \\ y=3x+5\\ x=3y+5\\Solve\;for\;y`

`\multimap\quad \tt x=3y+5\\x-5=3y\\\cfrac{x-5}{3}=y`

Why doesn't our answer show up among the answer choices? Has all of our hardwork been in vain?

Ofc not! There's just one more thing that can be done to simplify our answer.

`\tt \cfrac{x}{5}-\cfrac{5}{3}`

We're getting closer!

`\tt \cfrac{1}{3}x-\cfrac{5}{3}`

Voila! There's our answer, cheers! (;

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Hope I helped!

Best wishes.

Reach far.

Aim high.

Dream big.

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