Solving Square Area, Function Inverses, and Rational Functions Explained

question one the area a of a given Square can be represented by function a of P = p² / 16 p is greater than or

equal to zero where p is the perimeter of the square the graph of a function for p greater than equal to0 less than

or equal to 20 is shown below a find the values of a of 20 and inverse of a of 12 a of for

20 we will change every single P into 20 20 squar over 16 =

25 inverse of f of a this a is y and y equal f of x which

means f of x = a so inverse of a of 12 we are looking for a of P equal

12 a of P equals p² over 16 = 12 go to calculator control

divide p² over

16 = 12 control menu enter enter

enter P equals 13.9 by solver P =

13.9 which means the inverse a of 12 equals 13.9 B draw the graph of a inverse

function on the grade first step we need to draw y = x so find 4 4 8 8 12

12 16 16 2020 draw this thought to the line the

intersections for these two graphs will be the points on the inverse function on the original

graph we need to get some more coordinates 8 4 we will switch into

48 F the four fun8 is here then we can sketch the graph like this

normally three points determine a curve in the context of the question explain the meaning of inverse a of four =

8 we do know this is a y and here is x in this function area is y

then perimeter is X which means uh the square whose area is

four has a perimeter of eight question two a function is defined by 7 - 4 < TK x + 5 determine the domain

since this is a square root of function domain is to make

radic x + 5 greater than or equal to zero so X greater than or equal to -5 range

constant number is a seven so y here is a seven a is

A4 y less than or equal to 7 we can put this into graphing calculator to figure out domain and

range 7 minus 4

square root x + 5 enter let's change the window go to four

zoom out we will make inside this square root equals zero so x = 5 go to menu

five enter -5 enter we will get this uh starting

point 57 so X greater than or equal to -5 Y is a less than or equal to 7 find the value

of inverse of f of -2 of 6 + 7 inverse of f of a means f of x =

a we will set up F ofx = -2 6 + 7 f ofx is 7 - 4 < TK x + 5 =

-2 6 + 7 we will type this uh equation into this uh calculator control menu keep

enter x = 3.5 so inverse of f of 2 of 6 + 7 =

3.5 question 3 G of x = 1 - 3 over y - a x h 22 is on the graph of G find the value of a plug back into this function

2 = 1- 3 over 1 - A * 2

simplify 2 = 1 - 3 over 1 - 2 a type the whole equation into this

calculator control menu enter enter enter a equal 2 so we got the function G of x = 1 - 3 over 1 -

2x B write down the domain and a vertical ASM toote line domain since this is a rational

function we will make a denominator not equal to zero minus one both sides -2X is not equal to -1 ided

by -2 both sides X not = to 12 so vertical ASM to line x = 1 / 2 say find the X and V intercept for x

intercept we will set up for G of x = z 1 - 3 over 1 - 2x = Z solve this by solver control

menu enter enter enter x = -1 netive one Z is a x

intercept for y intercept we need to figure out G of zero every single X tur into 0 1 - 3

over 1 - 2 * 0 1 - 3 over 1 is 3 = -2 so 0 -2 is the V

intercept D find the value of for G of5 and a inverse g of5 g

of5 change every single X into -5 1 - 3 over 1 - 2 * 5 go to calculator 1 minus control

divide 3 over 1 - 2 * 5

enter 8 over 11 for inverse of G of5 we do know inverse G of a

means G of x = a so we set how G of x =

5 1 - 3/ 1 - 2x = 5 type the equation into

calculator control menu enter enter enter X = 0.25 which means the inverse G

of-5 = 0.25