Let f , g : R → R be defined, respectively by f (x) = x + 1, g (x) = 2x - 3. Find f + g, f - g and f/g

Solution:

Since f , g : R → R is defined as

f (x) = x + 1, g (x) = 2x - 3

Hence,

(f + g)(x) = f (x) + g (x)

= ( x + 1) + (2x - 3) .

= 3x - 2

Therefore, (f + g)(x) = 3x - 2

Now,

(f - g)(x) = f (x) - g (x)

= ( x + 1) - (2x - 3)

= x + 1 - 2x + 3

= - x + 4

Therefore, (f - g)(x) = - x + 4

Now,

f (g/x) = f (x)/g (x), g (x) ≠ 0, x ∈ R

= (x + 1) / (2x - 3), 2x - 3, x ≠ 3/2

Therefore,

f (g/x) = (x + 1)/(2x - 3), 2x - 3, x ≠ 3/2

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NCERT Solutions Class 11 Maths Chapter 2 Exercise ME Question 7

Let f , g : R → R be defined, respectively by f (x) = x + 1, g (x) = 2x - 3. Find f + g, f - g and f/g.

Summary:

Hence the values of f + g, f - g and f/g are 3x - 2, - x + 4 and (x + 1)/(2x - 3), 2x - 3, x ≠ 3/2 respectively.