Multiple Choice QuestionsLet f and g be differentiable functions satisfying g′(a) = 2, g(a) = b and fog = I (identity function). Then f ′(b) is equal to
1/2
2
2/3
2/3
A.
1/2
Given fog = I
⇒ fog(x) = x for all x
⇒ f ′(g(x)) g′(x) = 1 for all x
f ′(g(a)) =1/g('a) = 1/2
⇒f(b') = 1/2
The area of the region bounded by the curves y = |x – 2|, x = 1, x = 3 and the x-axis is
1
2
3
3
Let A (2, –3) and B(–2, 1) be vertices of a triangle ABC. If the centroid of this triangle moves on the line 2x + 3y = 1, then the locus of the vertex C is the line
2x + 3y = 9
2x – 3y = 7
3x + 2y = 5
3x + 2y = 5
Switch
is equal to
then the value of I2/I1 is
