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 numbersentence.Justify your reasoning.

Answer:a) f(x) = x^2b) f(x) = xc) any pair of numbersStep-by-step explanation:HI!a)an example of this kind of function is f(x) = x^2 becausef(x+h) = (x+h)^2 = x^2 + h^2 + 2 xh = f(x) + f(h) + 2xhteherfore f(x+h) ≠ f(x) + f(h)other example is f(x) = x^n with n a whole number different than onee.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 indicatedf(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 sectionlest consider 10 and 5f(10+5) = 2 *(10+5) = 2*15 = 30f(10) = 2*10 = 20f(5) = 2*5 = 10f(10) + f(5) = 20+10 = 30 = f(10+5)