Let ƒ and g be differentiable functions on R such that fog is the ide

1.	Let ƒ and g be differentiable functions on R such that fog is the identity function. If for some a, b ∈ R, g'(a) = 5 and g(a) = b, then ƒ'(b) is equal to : (1) 2/5 (2) 1 (3) 1/5 (4) 5
Answer» Answer is (3) 1/5 f(g(x)) = x f'(g(x)) g'(x) = 1 put x = a f'(b) g'(a) = 1 f'(b) = 1/5 Answer is (3) 1/5 f(g(x)) = x f'(g(x)).g'(x) = 1 x = a f'(g(a)) - g'(a) = 1 f'(b) = 1/5

Let ƒ and g be differentiable functions on R such that fog is the identity function. If for some a, b ∈ R, g'(a) = 5 and g(a) = b, then ƒ'(b) is equal to : (1) 2/5 (2) 1 (3) 1/5 (4) 5

Answer»

Answer is (3) 1/5

f(g(x)) = x

f'(g(x)) g'(x) = 1

put x = a

f'(b) g'(a) = 1

f'(b) = 1/5

Answer is (3) 1/5

f(g(x)) = x

f'(g(x)).g'(x) = 1

x = a

f'(g(a)) - g'(a) = 1

f'(b) = 1/5

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Let ƒ and g be differentiable functions on R such that fog is the identity function. If for some a, b ∈ R, g'(a) = 5 and g(a) = b, then ƒ'(b) is equal to : (1) 2/5 (2) 1 (3) 1/5 (4) 5

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