Let f(x) = 0 if x < 0 x if 0 ≤ x ≤ 1 2 − x if 1 < x ≤ 2 0 if x > 2 and g(x) = x f(t) dt 0 . and g(x) =  x f(t) dt   0 . (a) Find an expression for g(x) similar to the one for f(x).

Q: Draw the graph of f(x) and discuss its differentiability at x = 1

A: It is given that fx=x2x≤1xx&gt;1. Recall the fact that formula for derivative of a function f at a…

Q: Let f(x) f-¹(x) = 1 x + 11

A: we need to find the inverse of the function.

Q: How can I explain what it means for a function f(x) to be O(1)?

A: The 'f(x) to be O(1)' is to be read as function f(x) is of the order of 1.  Now refer to step two to…

Q: you agree with the contention that the functions f(x)= x +2 and g(x)= x2 -4/x-2  are the same in…

A: Yes i agree with the contention that the functions f(x)= x +2 and g(x)= x2 -4/x-2  are the same in…

Q: Find f(x) and g(x) such that h(x) = (f o g)(x). Let g(x) = 3x + 1. 1 h(x) = V3x + 1 f(x) =D

A:

Q: Let g(x) = VT + 3.

A: Given,  g(x)=x2+3

Q: 1 x-2 f(x)=- y g(x)=√x

A: To find the composite function

Q: Assuming f of g = 1/x + 1 and if g(x) is x +1. Find f(x)

A:

Q: ,x2

A:

Q: Let f(x) ƒ-¹(x) = = 1 x + 13

A:

Q: Find where f(x) = 1-ax x(x-a)(x+b) is discontinuous.

A:

Q: Let ƒ(x) = x/x - 2. Find a function y = g(x) so that (ƒ ∘ g)(x) = x.

A:

Q: If f(t) = (t2 + 1)(2t - 3et), determine the first derivative of f(t). a. (t2 + 1)(2 - 3et) + (4t2 -…

A: Given function for derivative f( t ) = ( t2 + 1 )( 2t - 3et )Formula used ddx( u.v ) = udvdx +…