Let f : R→R be defined by f(x) (3x+5) =and C = {x: 7.2< x <16.7}. Find (i) f(C) (ii) f ^-1(C)

Answer 1

The Function is f(x) = 3x+5

To find the inverse of the function, Let us assume f(x) = y and solve x in terms of y.

y =3x + 5

y - 5 = 3x

x = (y - 5)/3

Now interchange x and y.

y = (x - 5)/3

Replace y by  f^-1(x).

f^-1(x) = (x - 5)/3

C = {x: 7.2 < x < 16.7}

Substitute x = C.

f(C) = 3C + 5.

f^-1(C) = (C - 5)/3

Let us draw the table for f(C) and f^-1(C).

C	8	9	10	12	13	15	16
f(C)	29	32	35	41	44	50	53

Now for the inverse function, the domain is the range on the function f(C)

C	29	32	35	41	44	50	53
f-1(C)	8	9	10	12	13	15	16

Therefore C = f(f^-1(C)) = f^-1(f(C)).