PLEASE HELP!
Which of the following statements have the same result? Explain each step in solving each one.

f(1) when f(x) = 5x + 1
f-1(3) when f(x) = 2x plus 3, all over 5
3y - 7 = y + 5

Question

PLEASE HELP!
Which of the following statements have the same result? Explain each step in solving each one.

    f(1) when f(x) = 5x + 1
    f-1(3) when f(x) = 2x plus 3, all over 5
    3y - 7 = y + 5

anonymous · Answer

@chosenmatt @ganeshie8

kamibug · Answer

Let's look at the first one. :)
f(1) when f(x) = 5x +1
All they want you to do here is substitute 1 for x. 
f(1) = 5(1)+1 
f(1) = ?

anonymous · Answer

oh okay so the first one is 6. that was easy. what about the second one?

kamibug · Answer

Great! :) In the second one, when you see that superscript -1 on the f, that means you're looking for the inverse of the function. Do you know the steps to find the inverse of a function?

anonymous · Answer

do you replace f(x) with y?

kamibug · Answer

You got it! That's the first step! :) So we have $$y = \frac{ 2x+3 }{ 5 }$$ Do you know the next step?

anonymous · Answer

then you make it x=2y+3/5. right?

kamibug · Answer

Correct, we replace the x and y. :) And what's next? :)

anonymous · Answer

would it be 5x-3=2y? this is the part i get confused.

kamibug · Answer

After switching the places of x and y, we want to solve for y. To do that, we need to get it isolated on one side of the equal sign by using inverse operations. :) Just like we'd solve any other equation for a variable. 
x=2y+3/5
5x = 2y+3
5x - 3 = 2y
5x - 3 / 2 = y 
So the only thing you were missing was dividing both sides by two! =^.^=
Now that we've isolated y, the last step is to change y back to f(x).
f-1(x) = 5x - 3 / 2
So this new equation you found is the inverse of f(x). :) 
But when we look back at the problem, it says to find the inverse of f(x) when x = 3. So, like the first problem, now we just gotta substitute in the value of x. :) Think you got that?

anonymous · Answer

so it would equal f-1(3)=6 ?

anonymous · Answer

so f(1) when f(x) = 5x + 1 and f-1(3) when f(x) = 2x plus 3, all over 5, would be the two that are equal right :) @KamiBug

kamibug · Answer

Absolutely! :) We know the first two have equal values. But we need to check the last one also. The question wants you to solve each individually. The last one is the easiest. All you gotta do is solve the equation for the variable. Got this one? :) 
   3y - 7 = y + 5

anonymous · Answer

y=6. oh so all three are equal. okay cool! thank you so much for your help! really appreciate it! (:

seb.cal · Answer

People like you are the reasons why I pass my exams @KamiBug ;)