Let f : R→R, g : R→R and h : R→R be differentiable functions such that f(x) = x^2 + 3x + 2, g(f(x))

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Let f : R→R, g : R→R and h : R→R be differentiable functions such that f(x) = x2 + 3x + 2, g(f(x)) = x and h(g(g(x))) = x for all x ∈R  . Then

(a)  g’(2) = 1/15

(B)  h’(1) = 666

(C)  h(0) = 16

(D)  h(g(3)) = 36

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Correct option (b),(c)

Explanation :

(A) It is given that f: R→R, g: R→R and h: R→R are differentiable functions.

Now, f(x) = x3 + 3x+ 2 Differentiating w.r.t. to x, we get

f '(x) = 3x2 + 2

Also,

g(f(x)) = x

Now,

Now,

Hence, option (A) is incorrect.

(B) For all x  ∈ R :

Therefore,

Hence, option (B) is correct.

Hence, option (D) is incorrect