Application of DerivativeHard
Question
If f : [1, 10] → [1, 10] is a non-decreasing function and g : [1, 10] → [1, 10] is a non-increasing function. Let h(x) = f(g(x)) with h(1) = 1, then h(2)
Options
A.lies in (1, 2)
B.is more than 2
C.is equal to 1
D.is not defined
Solution
x > 1 ε f(x) ≥ f(1)
x > 1 ⇒ g(x) ≤ g(1)
⇒ f(g(x)) ≤ f (g(1)) .... (i)
Range of h(x) is subset of [1, 10]
⇒ h(x) ≥ 1 .... (ii)
By (i), (ii) we have h(x) = 1 ⇒ h(2) = 1
x > 1 ⇒ g(x) ≤ g(1)
⇒ f(g(x)) ≤ f (g(1)) .... (i)
Range of h(x) is subset of [1, 10]
⇒ h(x) ≥ 1 .... (ii)
By (i), (ii) we have h(x) = 1 ⇒ h(2) = 1
Create a free account to view solution
View Solution FreeMore Application of Derivative Questions
The coordinates of the points on the curve x = a (θ + sin θ), y = a (1−cos θ), where tangent is inc...If tangents are drawn from the origin to the curve y = sin x, then their points of contact lie on the curve...If the equation $a_n x^n + a_{n-1} x^{n-1} + \ldots + a_1 x = 0$, where $a_1 \neq 0$ and $n \geq 2$, has a positive root...The equation of the normal to the curve 2y = 3 − x2 at (1, 1) is-...The curve y = f(x) which satisfies the condition f′ (x) > 0 and f′′ (x) < 0 for all real x, is:...