Answer:
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)
