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Consider f : R → R given by f(x) = 4x + 3. Show that f is invertible. Find the inverse of f.

solution:

Think about f : R → R given by f(x) = 4x + 3

Say, x, y ∈ R

Let f(x) = f(y) then, at that point 4x + 3 = 4y + 3

x = y

f is one-one capacity.

Let y ∈ Range of f y = 4x + 3

or on the other hand x = (y-3)/4

Here, f((y-3)/4) = 4( (y-3)/4) + 3 = y This suggests f(x) = y

So f is onto

Subsequently, f is invertible.

Opposite of f is x = f – 1 (y) = (y-3)/4.