Help with algebra 2 problem???Please HELP???

Question

Find the inverse function of each function:

* y = 4

*F(x) = 3x

*g(x) = 3x - 1

Answer 1

Inverses:
y = 4. This has no inverse. It is not a 1-1 function.
That means the same y value is taken more than once
no matter what x is.

y = 3x.
Draw the graph. You will see that no horizontal
line hits it twice. So it has an inverse.
How to find it?
1). Solve for x:
x = y/3
2). Interchange x and y:
y = x/3

3). y = 3x -1. This is also 1-1 because
no horizontal line hits the graph twice.
To find the inverse proceed as in part 2:
y + 1 = 3x
x = (y+1)/3.
Now interchange x and y:
y = (x+1)/3

Hope that helped!

Answer 2

Inverses:
y = 4. This has no inverse. It is not a 1-1 function.
That means the same y value is taken more than once
no matter what x is.

y = 3x.
Draw the graph. You will see that no horizontal
line hits it twice. So it has an inverse.
How to find it?
1). Solve for x:
x = y/3
2). Interchange x and y:
y = x/3

3). y = 3x -1. This is also 1-1 because
no horizontal line hits the graph twice.
To find the inverse proceed as in part 2:
y + 1 = 3x
x = (y+1)/3.
Now interchange x and y:
y = (x+1)/3

Hope that helped!

Answer 3

There is no inverse to the first equation because it is not "one-to-one".

if f(x) = 3x, then the inverse function f(y) = y/3

if g(x) = 3x - 1 then the invers function is found by adding 1 to both sides and then multiplying by 3: g(y) = (y+1)/3.

Answer 4

y = 4 doesn't have inverse since is not one-to-one
For F...
Denote 3x = y then solve for x. You get x = y/3. Now switch x with y and the inverse of F, is F^(-1)(x) = x/3

For g do as above.

Answer 5

Just switch x and y

1) x=4

2) y=x/3 (also, x=3y, f(x)=x/3, or f(y)=3y)

3) y=(x+1)/3 (also, x=3y-1, g(x)=(x+1)/3, or g(y)=3x-1)

Answer 6

for the first one, the inverse would be y=1/4
second would be y=x/3
third would be y = (x+1)/3