Let f: x → y, where x and y are the set of all real numbers, and x and h are real numbers.
a. find a function f such that the equation f(x + h) = f(x) + f(h) is not true for all values of x and h.
b. find a function f such that equation f(x + h) = f(x) + f(h) is true for all values of x and h.
c. let f(x) = 2x. find a value for x and a value for h that makes f(x + h) = f(x) + f(h) a true number
sentence.
justify your reasoning.

a) f(x) = x^2

b) f(x) = x

c) any pair of numbers

Step-by-step explanation:

HI!

a)

an example of this kind of function is f(x) = x^2 because

f(x+h) = (x+h)^2 = x^2 + h^2 + 2 xh = f(x) + f(h) + 2xh

teherfore

f(x+h) ≠ f(x) + f(h)

other example is f(x) = x^n with n a whole number different than one

e.g.

f(x)=x^3

f(x+h) = (x+h)^3 = x^3 + h^3 + 3(x^2 h + x h^2) ≠ x^3 + h^3 = f(x) + f(h)

b)

f(x) = x is a function that actually behaves as indicated

f(x+h) = x + h = f(x) + f(h)

others examples of this kind of fucntion are given by multiplying x by any number:

f(x) = ax;    f(x+h) = a(x+h) = ax + ah = f(x) + f(h)

c)

Any pair of numbers will make f(x+h) = f(x) + f(h), as mentioned in the previous section

lest consider 10 and 5

f(10+5) = 2 *(10+5) = 2*15 = 30

f(10) = 2*10 = 20

f(5) = 2*5 = 10

f(10) + f(5) = 20+10 = 30 = f(10+5)

did you get the answer yet?

step-by-step explanation:

the final amount you will pay is $68.04.

the tip is determined by the pre-tax amount, so we calculate the tip based on the original bill, not after we've added sales tax.

to find the tip:

we can divide 54.00 by 100 to get 1% of 54. then we multiply that by 18.

54 / 100 = .54

.54 x 18 = 9.72

tip = 9.72$

to find the tax:

we can divide 54.00 by 100 to get 1% of 54. then we can multiply that by 8 to get 8%.

54 / 100 = .54

.54 x 8 = 4.32

tax= 4.32

now we can add the tip and tax to the bill to get our total.

54 + 9.72 + 4.32 = 68.04

total: $68.04

step-by-step explanation: