- {:.. Sx, x + 1, x> 1. x <1 Let f(x) = y=x+1 y=fx) a. Let e = 1/2. Show that no possible 8 > 0 satisfies the fol- lowing condition: |f«) – 2| < 1/2 whenever 0 < |x – 1| < 8. That is, for each 8 > 0 show that there is a value of x such that 0 < |x – 1| < 8 |f(x) – 2| = 1/2. and This will show that lim, 1 f(x) # 2. b. Show that lim,¬1 fX) # 1. c. Show that lim,¬1 fx)# 1.5.

Q: For all functions f and g, f o g(x) = go f (x). O True O False

A:

Q: Let f(x) f-¹(x) = 1 x + 11

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

Q: Let f(x) = (x-9)7 – 8, determine f¯¹(x). - ƒ¯¹(x) =

A: To find the inverse of the function f(x) = (x - 9)7 - 8, we need to express x in terms of y, where y…

Q: Each function f is defined as f : R - R. Prove why each of the functions is one to one or not one to…

A: See the attachment

Q: - Find and classify the discontinuities of the function f(x) x2 - 1

A:

Q: Prob. 5 (a) () Find all points where f is discontinuous. Classify these points (if any) as removable…

A:

Q: Each function f is defined as f :R +R. Prove why each of the functions is one to one or not c one.…

A: We will check the one to one of these functions

Q: Determine the values of x for which f(x) is continuous. Write the answer in interval notation. if x…

A:

Q: Let f(x) = 8 - x f-¹(x)

A:

Q: both an even and odd number function, then show that f(x)=0 at each point in its domain

A:

Q: et f(x) xeX. Use calculus to find all the x-values at which f has an inflection point. %3D

A:

Q: Let f(x) f-¹(-2) = x + 3 x + 6

A:

Q: Find the domain of the function. h(x) = In x + In(2 - x)

A: Given h(x)=ln x+ln (2-x) Find the domain by finding where the expression is defined.

Q: Let f be a function of x. f (x) = (x – 3)4 is an even function. - O True O False

A: Solution: The objective is to determine whether the given function is even or not

Q: Let f(x) ƒ-¹(x) = = 1 x + 13

A:

Q: Let f(x) = . Find all intervals where f is concave up and all intervals where it is concave down.

A:

Rate of Change

The relation between two quantities which displays how much greater one quantity is than another is called ratio.

Slope

The change in the vertical distances is known as the rise and the change in the horizontal distances is known as the run. So, the rise divided by run is nothing but a slope value. It is calculated with simple algebraic equations as: