Question

# 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)

Hint:

### f, g : R→R are the two functions and the fog or f(g) is the composite function of f and g .

## The correct answer is: 2x – 2

### We have given the function

f(x) = x + 1

g(x) = 2x – 3

We have to find the value of

i) f(x) + g(x)

ii) f(x) – g(x)

iii) f(g(x))

Therefore,

i) f(x) + g(x) = x + 1 + 2x – 3

= 3x – 2

ii f(x) – g(x) = x + 1 – (2x – 3)

= x + 1 – 2x + 3

= 4 – x

iii) f(g(x)) = f(2x -3)

= (2x – 3) + 1

= 2x – 2

Therefore, f+g = 3x – 2

f – g = 4 – x

f(g) = 2x – 2

We have to find the value of

Therefore,

Therefore, f+g = 3x – 2

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