Question

Can someone please tell me how to get the inverse?

Answer 1

Yeah, so, we know that the function has an inverse because it passes the horizontal line test. Now all we need to do is change x and y. Then get y by itself.

Remember, f(x) is y.

x = (-3/2)y + 7/2

(-3/2)y = x - 7/2

y = (x - 7/2)(-2/3)

y = -2/3x + 7/3

Answer 2

A function is a little like a road map - we put in a starting point (x) and we can follow the map's directions (the formula) to arrive at an end destination ( f(x) ).

I'm gonna recalibrate our map first to make it easier to see where we're going:

$f(x)=-\frac{3}{2}x+\frac{7}{2}=\frac{-3x+7}{2}$

The directions given by this map tell us this:

1. Start at x
2. Multiply x by -3
3. Add 7 to -3x
4. Divide -3x + 7 by 2
5. Arrive at your destination f(x) = (-3x + 7)/2

If our function shows us how to get to some destination, an inverse shows us the return trip. We can find the inverse of f(x) then by stepping through all of our directions in reverse:

1. Start at f(x) = (-3x + 7)/2
2. Multiply (-3x + 7)/2 by 2
3. Subtract 7 from -3x + 7
4. Divide -3x by -3
5. Arrive at your destination x.

If we swap the starting point and end destination - we'll start at x and call our end destination g(x) this time:

1. Start at x
2. Multiply x by 2
3. Subtract 7 from 2x
4. Divide 2x - 7 by -3
5. Arrive at your destination g(x) = (2x - 7)/-3

Presented a little cleaner:

$g(x)=\dfrac{2x-7}{-3}$