Question -
Answer -
Givenf: R → R given by f(x) = 4x + 3
Now we have to showthat the given function is invertible.
Consider injectionof f:
Let x and y be two elements of domain (R),
Such that f(x) = f(y)
⇒ 4x + 3 =4y + 3
⇒ 4x = 4y
⇒ x = y
So, f is one-one.
Now surjectionof f:
Let y be in the co-domain (R),
Such that f(x) =y.
⇒ 4x + 3 = y
⇒ 4x = y -3
⇒ x = (y-3)/4 inR (domain)
⇒ f is onto.
So, f is a bijection and, hence, it is invertible.
Now we have tofind f -1
Let f-1(x)= y……. (1)
⇒ x = f (y)
⇒ x = 4y + 3
⇒ x − 3 = 4y
⇒ y = (x -3)/4
Now substituting thisvalue in (1) we get
So, f-1(x)= (x-3)/4