#1**+1 **

4)

Let's write this as

y = ( 7 - 8x)^2

The idea is to get by itself and then "swap" x and y

Take the square root of both sides

±√y = 7- 8x subtract 7 from both sides

-7 ±√y = - 8x divide both sides by -8 [ this has no affect on the " ± " ]

[ 7 ±√y ] 8 = x "swap" x and y

[ 7 ±√x ] / 8 = y for y, write f^{-1}(x)

f^{-1}(x) = [ 7 ±√x ] / 8

This is not a function.....to see why, ..let x = 9

Note that we get 2 different y values here.....(9, 5/4) and (9, 1/2)

For something to be a function, we CANNOT have two different y values for the same x value !!!

So....the first answer is correct

Here's the graph : https://www.desmos.com/calculator/470f3qvli7

NSS.... this graph DOES NOT pass the "vertical line" test......if we can draw a vertical line that cuts the graph more than once at any point, we do not have a function

CPhill Feb 5, 2018

#2**+1 **

5)....This is kind of a "trick" question, NSS...it's not as tough as it appears

( g^{-1} o g) (4) means the same as g^{-1} (g(4) )

So

g(4) means that we are putting 4 into the function and evaluating

So we have 14 / [ 4 + 3 ] = 14/7 = 2

Now we have

g^{-1} (g(4) = g^{-1}(2)

Note that the inverse REVERSES the original coordinates...so....4 led us to 2 in the original function... (4,2).......so.......2 in the inverse leads us back to 4.....(2,4) !!!

So g^{-1} ( 2 ) = 4

CPhill Feb 5, 2018