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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)

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asked Dec 1, 2014 in BASIC MATH by anonymous

1 Answer

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(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  image.

image

C = {x: 1.3 < x < 16.6}

Substitute x = C.

f(C) = 7C + 1.

image

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

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

image

1.5 3 6 9 12 15 16.5

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

answered Dec 2, 2014 by Lucy Mentor

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