Let f : R→R be defined by f(x) = (7x + 1) and C = {x: 1.3< x <16.6}. Find 3. (i) f(C) (ii) f ^-1(C)

Answer 1

(1)

The Function is f(x) = 7x+1

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

y = 7x + 1

y - 1 = 7x

x = (y - 1)/7

Now interchange x and y.

y = (x - 1)/7

Replace y by  .

C = {x: 1.3 < x < 16.6}

Substitute x = C.

f(C) = 7C + 1.

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

C	1.5	3	6	9	12	15	16.5
f(C)	11.5	22	43	64	85	106	116.5

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

C	11.5	22	43	64	85	106	116.5
	1.5	3	6	9	12	15	16.5

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