Z is the set of integers, R is the set of real numbers. 1. Functions f, g, and h are defined as f:R + R, g :R -R. h:R +R, h(r) = V + 25 f(z) =r+ 10 9(z) = 10 (ho f)(3) (go f)(z) 2. For each of the following functions prove whether they are One to one, and Onto. If they are not one to one or onto, show why. f:R+ +Rt, f(z) = r.

Q: Give the domain of the function. z = 4x – 5y O {(x, y): x and y are real and 4x – 5y = 0} O {(x, y):…

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Q: 2. If p and q are positive integers, f is a function defined for positive numbers and attains only…

A: Introduction :

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Q: Suppose that the function f is defined, for all real numbers, as follows. if x1 Find f(-2), f(-1),…

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Q: 2. Determine whether f is a function from Z to R if a) f(n) =±n. b) f(n) = Vn²+1. c) f(n) = 1/(n² –…

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Q: A fX-Y where X,Y e Z* , and 0s<X <23 and, 0<Y<59, X is hour of clock and Y is minute of digital…

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Q: 2. Determine whether the function y= -x5 + x3 – 1 is even, odd, or neither. Justify your ans wer.

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Q: Which is the correct conclusion about the function h(x) ={V4- x2 if x - 3 if h has a removable…

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A: Topic = Function

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Q: Suppose that the functions s and t are defined for all real numbers x as follows. s (x) = 4x+6 t(x)…

A: Given functions are: -----------------------------------------------------------------------------…

Q: Consider the following statements 1- The function f defined by f(x) = x³ is decreasing in R 2- If a…

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Q: Suppose f and g are contimuously differentiable functions such that f(x) = d(x) and g(x) f(x) and…

A: Define a new function                                                   r(x) = f2(x) -…

Q: (a) Prove or disprove: f: Z3 → Z5, [x]3 → [x³]5 is well defined. (b) Prove or disprove: f: Z10 →…

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Q: For the function f (x) = |x| defined on [-1,1], there is some -1<c<1such that f' (c) = 0. O True…

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Q: Suppose that the functions s and t are defined for all real numbers x as follow s (x) =x-3 t (x) =…

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Q: Suppose that the function h is defined on the interval (-2, 2 as follows. (-1 if -2<rs-1 if –1 <x<0…

A: Solve the function

Q: Let f(x)={x2+2x+1, if x≤3 ax+b,if x>3 Find a and b such that the function f(x) is differentiable…

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Q: 8. Show that the function f : N → Q defined by f(n) n- is one to one. n+1

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Q: Which of the following statements is TRUE about f(x)= |2x-4|? a) f'(x) = 2, for all x not equal to…

A: Given expression is  f(x)=|2x-4|

Q: Suppose that the functions s and t are defined for all real numbers x as follows. s(x)%3D4X-2…

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Q: [3) is defined by f (x) = 15, Зх +4 and 5х-7 Show that if f:R- →R- 7x+4 8:R- is defined by g(x) = ,…

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Q: Let f(x)  = 1- x2/3 . Show that f(-1) = f(1) but there isno number c in  (-1, 1)such that  f'(c) =0…

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Q: Suppose that the function h is defined on the interval-2, 2) as follows. -2 if-2<x<-1 -1 if-1<x<0 h…

A: Given:     To determine: h(-2), h(-1.5), h(1)

Q: Suppose that the functions s and t are defined for all real numbers x as follows. s (x) =x-5 t (x)=…

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Q: Suppose that the function f is defined, for all real numbers, as follows. 3 if x + 1 f(x) = 2 if x =…

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Q: If we apply Rolle's Theorem to the function f(x) = 2x- 16x 6 on the interval [2, 6|, how many values…

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Q: 2. If p and q are positive integers, f is a function defined for positive numbers and attains only…

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Q: 1. Define h(x) = +y7x + 2, for all real numbers x > -. (a) Is h a one – to – one function? Why or…

A: Since not a particular question asked ,as per guidelines solution to only first question is given

Q: Suppose that the functions s and t are defined for all real numbers x as follows. s (x) = 4x-3 t (x)…

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Q: Suppose that the function h is defined on the interval (-2.5, 1.5) as follows. -2 if -2.5<x<-1.5 -1…

A: We can answer all the three questions as below.

Q: Suppose that the functions s and t are defined for all real numbers x as follows. s s (x) =x+1 1 (x)…

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Q: Let f:2+ +2 be the function defined by if n>l00 f(f (nt 11)) othe rwise fln) =d n-10 what is the…

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Q: For any positive integer n show that 1 n + 1 holds for any f e C'[0, 1] satisfying f(0) = 0. Verify…

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Q: 8. Decide if the following functions are onto. Prove your answers. (a) f(x) = x² – 1 (b) g(x) = 2x…

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Q: Suppose that the function /i is defined, for all real numbers, as follows. 2 ifx+-2 h (x) = -2 if…

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Q: Suppose that the function f is defined, for all real numbers, as follows. -1 if x<-1 sW*+1)*+2…

A: a) For f(1),  f(x) = -(x+1)2 +2  f(1) = -(1+1)2 +2         = -4 +2          = -2  So, f(1) = -2

Q: For the function def ined by f (x) =x² on [0, 1] and P=0,-,- 4 4 4 1, then: U(f;P)=[X]

A: We will find U(f,P) for the partition

Q: If f (x) and g(x) then there exists a constant C such that f(x) = 9(x)+C, for all x. are two…

A: Let us consider h(x) = f(x) - g(x), Then h'(x) = f'(x) - g'(x) Since we have given f'(x) = g'(x),…

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Q: If the function f:R → R given by f(x) =x³+ax²+bx+5sin*is an increeasing function , Find the…

A: if F(x) is increasing function, then F'(x) must be greater than 0. So from that, we will solve this…

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Q: Suppose that the functions s and t are defined for all real numbers x as follows. s(x) = x+ 1 t(x) =…

A: Given,  sx = x+1  tx = 3x+2  We have to write the expression for  s+tx,  s-tx  and s.t4 .