Question

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

f(3) when f(x) = 2x + 2
f−1(4) when f(x) = 3x minus 4, all over 5
y + 10 = 2y + 1

Answer 1

f(3) when f(x) = 2x + 2
f−1(4) when f(x) = 3x minus 4, all over 5


You should probably solve them to have an idea xD

Answer 2

Do you know what this
`f(3) when f(x) = 2x + 2`
refers to?

Answer 3

sorry ive been solving it by my self i think i got this but would you check my answers? this is what i have so far

Answer 4

Okay sure

Answer 5

alright this is my over all answer

Answer 6

I. find f(3) we are going to replace x with 3 so it would look like this
f(3)=2(3)+2 once we have this we multiply 2*3 which equals 6 and we plug that in.
(3) = 6 + 2 then we add 6+2 which equals 8 which is our answer
f(3) = 8

II.find f^-1(4) we are going to replace f(x) with y once we have this we are going
y = (3x - 4)/5 to take our equation and swap the variables putting x on the outside
x = (3y - 4)/5 and y on the inside next we have to solve for y. which equals
5x = 3y - 4 next we swap sides and place 5x -4 on the left side of the = sign then
5x + 4 = 3y turn the - into a + turn it into a fraction by placing (5x+4) over 3
(5x + 4) over 3 = y
f^-1(x) = (5x + 4) over 3 Once you have (5x+4) over 3 we are going to take f^-1(x)
f(4) = (5(4) + 4)/3 and replace it with f(4) we then add 4 on both sides and solve
f(4) = (20 + 4)/3 this equals 5*4=20 then 20+4=24 which makes the fraction 24/3
f(4) = 24/3 we then divide 24 by 3 which equals 8
f(4) = 8


III.
y + 10 = 2y + 13 we are going to start by subtracting 10 from both sides
y+10-10=2y+1-10 then we simplify
y=2y-9 we then subtract 2y from both sides
y-2y=2y-9-2y we then simplify again
-y=-9 then we divide by -1
-y -9

Answer 7

You don't have to swap the sides mid step but if it helps then yes

Looks good though

Answer 8

Thank you dude im actually proud of my self with how this turned out you guys are alot of help here :D