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a)    f(x)   = (9/5)x - 4

Write f(x)   as "y"........the idea is to get x by itself and then "swap" x and y .......so we have...

y = (9/5)x  - 4      add 4 to both sides

y + 4  = (9/5) x    multiply both sides by 5/9

[5 (y + 4) ] / 9    =  x         "swap" x and y

[5 (x + 4)] / 9   = y     for y, write  f^-1(x)  

[5 (x + 4)] / 9  = f^-1(x)

And this is the inverse

So   f^-1(20)  = [5 (20 + 4)] / 9   = [ 120]/ 9

b)  g(x) =   4x^2 + 8x + 13   .....this function is not "one-to-one"..........no inverse exits

c)  h(x)  =   1 / √x     this function is one to one.....but the domain is restricted to x > 0

y = 1/ √x   square both sides

y^2  = 1 / x    "swap"  x and y

x^2  = 1 / y        rearrange as

y =   1/ x^2     for y, write  h^-1(x)

h^-1(x)  = 1/x^2   

So   h^-1(4)   =  1/(4)^2   = 1/16

Thanks CPhill!

4* pi * r*r*r *h

 ___________

          3

Is there a way to not make it run off the page?

Oh! I thought it would show it. 

Sorry, Dabae, but the LaTex coding runs off the page  on my computer and I can only see part of each question......!!!!

If it depreciates at 7% per year, then its value the subsequent year is only 93% of that of the previous year........so.....the value after five years =

75000 * (.93)^5   = about  $52,176.63

FV=PV [1 - .07]^5

FV=75,000 x .93^5

FV=$52,176.63 - its value after 5 years.

I think you may mean the cosine inverse.......usually designated as cos^-1    [or,  arccos ]

Just hit the "2nd"  button on the calculator and find the arccos  key

[77,777,770!] =1.5893392885… × 10^579,954,691.

P. S. Do you ANY IDEA how large a number that is????

85%   of 20 problems  =  .85 * 20    =  17 correct

Just google "Scientific Caculators".

2/7 ths of the time it lands on "heads"......then......it must land on "tails" the other 5 times....so....

5/7  = probability of getting  "tails"  = about  .714    = about 71.4 %

No prob, mathcalc.....!!!!

Thank you so much CPhill!

This is easiest to see if we imagine that there are 100 people in the town

75%   have  cell phones  = 75.......and 20% of these don't have computers 

So  .....  20% of 75 = .20 *75  = 15 who have cell-phones don't have computers

Here's the Venn diagram

So  60%  of the people own computers and cell phones  =  .60

We can solve this with a proportion

3.5 miles / ( 1/4  gallon)  =  1 mile  / x  gallons        ......  cross-multiply

3.5 * x  = (1/4) * 1     divide both sides by 3.5

x = (1/4) / 3.5          [note 3.5   =  35/10   = 7/2  ]

x = (1/4) /( 7/2)

x = (1/4) (2/7)   =   2/28 gallons  =  1/14 gallons

y = 4x

20 = 5(4)

20 = 20

Equation is correct.

y=4(2)

y=8

When x = 2, y = 8

-6-(-2)

-6 + 2

(Two negatives make positive)

-4

If a sequence is defined recursively by f(0)=2 and f(n+1)=-2f(n)+3 for n≥0, then f(2) is equal to? (1)1 (2)-11 (3)5 (4)17

f(0)   = 2

f(0 + 1)  =  f(1)   =  -2f(n) + 3 =   -2f(0) + 3  = -2(2) + 3  = -1

So

f(1 + 1)   = f(2)   = -2f(n) + 3  = -2f(1)  + 3  = -2(-1) + 3    =  5

use the carrot sign(^) and then the exponent

-6

71,021

What is 5a to the second power - 7

(5a)^2 - 7

25a^2 - 7