Let f : R → R be a function defined by
f(x) = Min {x + 1, |x| + 1}.
Then which of the following is true?
Give reason.

(1) f(x) ≥ 1 for all x ∈ R
(2) f(x) is not differentiable at x = 1
(3) f(x) is differentiable everywhere
(4) f(x) is not differentiable at x = 0

Question

Let f : R → R be a function defined by

f(x) = Min {x + 1, |x| + 1}.

Then which of the following is true?

Give reason.

(1) f(x) ≥ 1 for all x ∈ R

(2) f(x) is not differentiable at x = 1

(3) f(x) is differentiable everywhere

(4) f(x) is not differentiable at x = 0

Aditya Gupta · Answer

Due to |x| greater than equal to x for all x belonging to R, f(x)= x+1 So obviously it is differentiable everywhere on the real line

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Let f : R → R be a function defined by f(x) = Min {x + 1, |x| + 1}. Then which of the following is true? Give reason. (1) f(x) ≥ 1 for all x ∈ R (2) f(x) is not differentiable at x = 1 (3) f(x) is differentiable everywhere (4) f(x) is not differentiable at x = 0

Let f : R → R be a function defined by
f(x) = Min {x + 1, |x| + 1}.
Then which of the following is true?
Give reason.

(1) f(x) ≥ 1 for all x ∈ R
(2) f(x) is not differentiable at x = 1
(3) f(x) is differentiable everywhere
(4) f(x) is not differentiable at x = 0

1 Answers

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Let f : R → R be a function defined by f(x) = Min {x + 1, |x| + 1}. Then which of the following is true? Give reason. (1) f(x) ≥ 1 for all x ∈ R (2) f(x) is not differentiable at x = 1 (3) f(x) is differentiable everywhere (4) f(x) is not differentiable at x = 0

Let f : R → R be a function defined byf(x) = Min {x + 1, |x| + 1}.Then which of the following is true? Give reason. (1) f(x) ≥ 1 for all x ∈ R(2) f(x) is not differentiable at x = 1 (3) f(x) is differentiable everywhere(4) f(x) is not differentiable at x = 0

1 Answers

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Let f : R → R be a function defined by
f(x) = Min {x + 1, |x| + 1}.
Then which of the following is true?
Give reason.

(1) f(x) ≥ 1 for all x ∈ R
(2) f(x) is not differentiable at x = 1
(3) f(x) is differentiable everywhere
(4) f(x) is not differentiable at x = 0