Home
Class 12
MATHS
Let g(x)=[(3x^2-4sqrtx+1, x<1),(ax+b, x>...

Let `g(x)=[(3x^2-4sqrtx+1, x<1),(ax+b, x>=1))` If `g(x)` is continuous and differentiable for all numbers in its domain then (A) a=b=-4 (B) a=b=4 (C) a=4 and b =-4 (D) a=-4 and b=4

A

a = b = 4

B

a = b = -4

C

a = 4 and b = - 4

D

a = - 4 and b = 4

Text Solution

Verified by Experts

The correct Answer is:
C
Promotional Banner

Similar Questions

Explore conceptually related problems

Let h(x) = min {x, x^2} , for every real number of X. Then (A) h is continuous for all x (B) h is differentiable for all x (C) h^'(x) = 1, for all x > 1 (D) h is not differentiable at two values of x

If two different tangents of y^2=4x are the normals to x^2=4b y , then

Verify Mean Value Theorem, if f(x)= x^(2)-4x-3 in the interval [a, b] where a=1 and b= 4.

If x-1 is a factor of 2x^(3)+ax^(2)+2bx+1 and 2a-b=4 . Find the values of a and b.

The number of solutions of (log)_4(x-1)=(log)_2(x-3) is (2001, 2M) (a) 3 (b)1 (c) 2 (d) 0

The function f(x)=e^x+x , being differentiable and one-to-one, has a differentiable inverse f^(-1)(x)dot The value of d/(dx)(f^(-1)) at the point f(log2) is 1/(1n2) (b) 1/3 (c) 1/4 (d) none of these

If the area of the region bounded by the curve y= f(x) , X - axis and x=1 and x=b is (b-1) sin (3b+4) f(x) ……

Find x such that the four points A(3, 2, 1), B(4, x, 5), C(4, 2, -2) and D(6, 5, -1) are coplanar.

If a line x+ y =1 cut the parabola y^2 = 4ax in points A and B and normals drawn at A and B meet at C. The normals to the parabola from C other than above two meets the parabola in D, then point D is : (A) (a,a) (B) (2a,2a) (C) (3a,3a) (D) (4a,4a)

Let A = {-1,0,1,2}, B = {-4,-2,0,2} and f , g : A rarr B be functions defined f(x) = x^(2)-x, x inR and g(x) = 2 |x-(1)/2|-1,x inR . Are f and g equal ? Justify your answer. (Hint : One may note that two functions f : A rarr B and g : A rarr B such that f (a) = g(a) A a inA, are called equal functions).