INVERSES...... Help me please?

Question

This is the question:

http://img228.imageshack.us/img228/4946/poy33hm7.png

I don't know what it is asking. How can I solve it?

Answer 1

f(x) = 7-3x
f^(-1)(x) = 1/(7-3x)

so, f^(-1)(2), is just putting x=2 into the above formula, i.e.

f^(-1)(2) = 1/(7-3*2) = 1

Answer 2

I don't know why you went though all that trouble to upload an image you could have written out, but I digress.

First you have to find the inverse of f(x). Then you have to plug in 2.

To find the inverse, let y = f(x) and solve for x in terms of y.
y = 7 - 3x
y - 7 = -3x
-(y - 7)/3 = x
so f^-1 (x) = -(x - 7)/3, and
f^-1 (2) = -(2 - 7)/3 = -5/3

Answer 3

So, you have the function y = 7 - 3x. To find the inverse, you need to switch the places of y and x and solve for y:
x = 7 - 3y
3y = -x + 7
y = -(x/3) + (7/3)

Then, you plug in 2 for x:
y = -(2/3) + (7/3)
y = 5/3 =]

Answer 4

Let y = 7-3x
To find the inverse:
1). Solve for x
3x = 7-y
x = 7/3 -y/3
2. Swap x and y
y = 7/3 - x/3= f^-1(x)
So f^-1(2) = 7/3 -2/3 = 5/3.

Answer 5

f^(-1) is the inverse of f,
so if f(x) = x + 1, the inverse would be found by:
x = f(x) + 1
f(x) = x - 1
There are many other definitions of inverse functions, but that's the easiest and it works.

f(x) = 7 - 3x
****note: f(x) hereafter is f^-1 (x)
x = 7 - 3 f(x)
x + 3f(x) = 7 - 3 f(x) + 3 f(x)
3 f(x) + x - x = 7 - x
3 f(x) = 7 - x
f(x) = (7 - x)/3
f(2) = (7 - 2)/3
f(2) = 5/3

Answer 6

to find the inverse of the function f(x) = 7-3x
rearrange it as follows
f(x) = 7-3x
y = 7-3x
x = (7-y)/3
then f-1(x) = (7-x)/3
so f-1(2) = 5/3 or 1.667