Question

I'm doing a practice, and I'm really confused by this question. Help would really be appreciated!!! **100 PTS!**

Answer 1

Great Question!

The problem we have at hand is known to be a function, which maps elements from one set of objects, ( the domain ) onto another, the range. If we were to consider an ordered pair, say ( x, y ), then the function would map x onto y. The inverse function is simply the reverse. Take the ordered pair (-4,0). Function g would map - 4 onto 0, such that $g( - 4 ) = 0$. Therefore, the inverse function would map 0 onto - 4, resulting in $g^{-1}( 0 ) = - 4$. And there you have it! Our first part is answered!

____

This second bit here is interesting. Let $y = h( x )$ -

$y = 4x + 3$ - Switch x and y,

$x = 4y + 3$ - And now solve this equation for y,

$x - 4y = 3,\\- 4y = - x + 3,\\y = 1 / 4x - 3 / 4$

As you can see, we have taken the inverse of h( x ). As y = h( x ), we can thus conclude the following -

$h^{-1}(x) = 1 / 4x - 3 / 4$

____

The composition (h^-1 o h)(-5) is, in other words, h^-1(h(-5)). We can therefore calculate h(-5) and then take it's inverse -

$h(-5) = 4(-5) + 3,\\h(-5) = - 20 + 3,\\h(-5) = - 17$

Now we can take it's inverse -

$h^{-1}(-17) = 1 / 4( - 17 ) - 3 / 4,\\- 17 / 4 - 3 / 4,\\= - 5!$

Our solution for this last bit is - 5. And, if you don't feel like reading through this entire explanation just take a look at the " summed up " answer below,

$g^{-1}( 0 ) = - 4,\\\\h^{-1}( x ) = 1 / 4x - 3 / 4,\\\\( h * h^{-1} )( - 5 ) = - 5$  I do hope that helps you!

Answer 2

Answer:

Or 50

Step-by-step explanation: