Question

solve this problem...
Chapter - relations and functions

Answer 1

we have,
f: R to R given by f(x) = 4x + 3

For one- one,
let x, y belong to R (domain)
then, f(x) = f(y)
4x + 3 = 4y + 3
x = y
therefore, f is one - one


For onto,
let y belongs to R (co domain)

then, f(x) = 4x + 3
y = 4x + 3
4x = y-3
x = (y-3)/4
I.e., for every value of y there's unique value in x
therefore, f is onto
Thus, f is bijective


inverse of f:
since f(x) = y, f inverse of y = x
4x + 3 = y
x = (y-3)/4
f inverse y = (y-3)/4