Q. 45.0( 1 Vote )

# If f(x) = 2x + 5 and g(x) = x2 + 1 be two real functions, then describe each of the following functions:(i) fog(ii) gof(iii) fof(iv) f2Also, show that fof ≠ f2.

f(x)= 2x + 5 and g(x)= x2 + 1

The range of f = R and range of g = [1,∞]

The range of f Domain of g (R) and range of g domain of f (R)

both fog and gof exist.

(i) fog(x) = f(g(x)) = f (x2 + 1)

= 2(x2 + 1) + 5

fog(x)=2x2 + 7

Hence fog(x) = 2x2 + 7

(ii) gof(x) = g(f(x)) = g (2x + 5)

= (2x + 5)2 + 1

gof(x)= 4x2 + 20x + 26

Hence gof(x) = 4x2 + 20x + 26

(iii) fof(x) = f(f(x)) = f(2x + 5)

= 2 (2x + 5) + 5

fof(x) = 4x + 15

Hence fof(x) = 4x + 15

(iv) f2(x) = [f(x)]2= (2x + 5)2

= 4x2 + 20x + 25

from (iii) and (iv)

fof ≠ f2

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