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: Let f and g be functions such that f(0) = 18, f '(0) = 3, f(18) = 11, f '(18) = - 5 and g(11) = -…

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Q: 4. Let f(x)=1+x³-x. Find an x-value that makes f(x) 0.

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Q: Select which function f has an inverse g that satisfies g'(1) = Of(x) = 2x³ Of(x) == x³ Of(x) = x³…

A: To find the function  that has an inverse  that satisfies .

Q: Let f(x) and g(x) be defined as follows: f(x) = 2x+ 1, g(x) = /x-3 What is (fog)(x)?

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Q: If y = g(u) = u2 / (1-2u) and u = h(x) = x +5, determine the composite functions  (a). g(h(x))…

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Q: Let a, b 0. Find f(100) (a) provided that x³ (a - bx)²* f(x) =

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Q: Let f(x) = 4 – a?, a > 0 f- (x) =

A: Given:- f(x) =4-x2  To find:- f-1(x)

Q: Let n be a positive integer. Define the function fn(z) by dzn (2²+2x+2)". Find the value of fn(-1 +…

A: Solution:Given: Let be a positive integer. the function is defined bywe have to find the value of

Q: 5. Sketch the graph of one function f(x) that has all of the following properties: a.) f(-2) 0 b.)…

A: As per our guidelines we are supposed to answer  only one question. Here question 5) answer.

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

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Q: Find f′(0), where f(x)= (x|x|)/(2+⌊x⌋)

A: Consider the given function fx=xx2+x

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 +…

Q: Let f(x)= -x-1, h(x) = -x + 5. Find (h of)(2). (hof)(2) =

A: The answer is given below: Topic: Composite Function