Need help with functions real numbers etc Thanks Define f R

Need help with functions, real numbers, etc. Thanks!

Define f: R rightarrow R by f (x) = 4x - 1 for all x element R. Is f one-to-one ? Prove or give a counterexample. Define g: Z rightarrow Z by g(n) = n^2 for all n element Z. Is g one-to-one ? Prove or give a counterexample. Define f: R rightarrow R by f (x) = 4.x - 1 for all x element R. Is f onto ? Prove or give a counterexample. Define h: Z rightarrow Z by h (n) = 4n - 1 for all n element Z. Is h onto? Prove or give a counterexample.

Solution

f(x)= 4x-1

If we plug any value for x,we get a different value for f(x)

Therefore f(x)= 4x-1 is one to one function

b. g(n)= n^2

when n=1,g(n)=1

and when n=-1,g(n)=1

As we see that for different values of n we are getting same value of g(n), so its not one to one

c) f(x)= 4x-1

For every value of x,we got a value for f(x) and no same values of x have a value for f(x) here. So its onto

d) f(n)= 4n-1

Here again we have value for any value for n we get a value for f(n). So its onto