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Help.

Feb 5, 2018

#1
+100516
+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 !!!

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

Feb 5, 2018
#2
+100516
+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

Feb 5, 2018