For Exercise,  a.Write the domain and range of f in interval notation. b.Write an equation of the inverse function. c. Write the domain and range of f−1 in interval notation. f(x) = −x^2 + 1, x ≤ 0

Q: Determine whether the function is one-to-one. f(x) = 3 + x3

A: Given: f(x)=x3+3To determine whether f(x) is one-to -one are notFormula:(i) f(x)=f(y)⇒x=y   (f is…

Q: Given a function f, explain the difference between f(3) and f(x) = 3.

A: In f(3), 3 is in domain of f(x) and f(3) is value of a function f(x) at x=3.

Q: 1 f(x) = +3 -x+2

A: Topic = Functions

Q: Describe the end behavior of the function f (æ) = -2x+ 3x2 – 5a + 1. f (x) as x → ,f (x)→ as x →

A: We have to describe the end behavior of the function f(x)=-2x4+3x2-5x+1.

Q: Estimate how much the function f (x) = 1/1 + x2 will change if x decreases from 1 to .9.

A: Given: The function  f(x) = 11+x2 To find: How much the given function will change if x decreases…

Q: Suppose that function f divides x by 3 and adds 11. Write an equation for f−1(x).

A: Given, the function f divides x by 3 and adds 11.That is

Q: Write a relationship for a function whose f(x) values are 3 more than the principal square root of x

A: The principal square root of x=x 3 more than the principal square root of x=3+x Hence, The function…

Q: Specify the domain of the function f (x) = /2x + 14.

A: Given : fx = 2x+14

Q: Differentiate the function.  f(x) = 240

A: Given function is

Q: Determine whether the function is even, odd, or neither.   f(x)= 1x+12 x3

A:

Q: What is the inverse of the function f(x) = In (5x + 1) - 7?

A: Given query is to find the inverse of the function f(x).

Q: Determine whether the function is even, odd, or neither. f(x) = 4x + 2x3

A:

Q: what is the domain of the function f(×)=(×+1) ?

A: If y=f(x), then the variable x is called the input of the function, and y is called the output of…

Q: 17. Find the difference quotient for the function f(x)%=(x²+1) °, then simplify.

A: Given function is:

Q: Determine whether the function is even, odd, or neither.   f(x)= 1x+15 x3

A:

Q: Which table does not represent a function of x?

A:

Q: O f(x) = 5*

A:

Q: solve for the inverse of the function   f-1x format, please

A:

Q: If f(x) = 10, find f'(-1).

A: Given f(x)=10,  to find f'(-1) Formula used Differentiation of a constant value is zero d (constant)…

Q: Classify the functions as even, odd, or neither. ƒ(x) = 5x

A: Given function is fx=5x. To determine whether function is even, odd or neither. Solution: A function…

Q: Classify the functions as even, odd, or neither.

A: Given: f(x)=|x-2|

Q: Write f(x) = 2x 4 - 5x 3 + 12x2 - 3x + 4 as the sum of an even and an odd function.

A:

Q: How I write h(x)=x2-1 in a functions equation?

A: Consider the given function

Q: Refer to the function: f(x)=[x] dertermine f(-0.8)

A:

Q: Investigate when, historically, the use of the function notation y=f(x) first appeared.

A: Given, Investigate when, historically, the use of the function notation y=f(x) first appeared.

Q: what is the domain and range of the inverse function f-1(x)=-x/(3-7x)?

A:

Q: the perimeter of a rectangle is 190 inches, if the rectangle is x inches long, find the function for…

A:

Q: evaluate the function F(x) = 0.9x   when X=1.4

A: Given  F(x)= 0.9x  we need to substitute x=1.4 to given equation

Q: Determine whether the function is one-to-one. f(x) = x4 + 5, 0 ≤ x ≤ 2

A: To determine: Whether f(x)=x4+5 , 0 ≤ x ≤ 2 is one-to-one.

Q: Classify the functions as even, odd, or neither. ƒ(x) = x2 - 3

A: The given function is; ƒ(x) = x2 - 3

Q: Classify the functions as even, odd, or neither. ƒ(x) = 3x

A:

Q: Write the domain of the following function using interval notation. 3x-5 f(x) 4-3x

A:

Q: which rule is broken if multiplying f(x) by c gives the function f (cx)? keep the usual addition…

A: This is a kind of transformation   When multiplying a constant in the function then the function…

Q: What are the zeros of the function?

A:

Q: Which could be the table of values that was used to graph the function of x shown?

A:

Q: Is the function f(x) = x3 one-to-one?

A: Given: fx=x3 Horizontal line test: If no horizontal line intersects the graph of the function more…

Q: Is the function f(x)=x' +x-1 even, odd, or neither?

A:

Q: Determine if the function is even, odd or neither f(x) = x3 - x + 3

A: According to rules of even or odd functions, if f(-x) = f(x), it's an even function, if f(-x)=…

Q: Verify algebraically whether the function is even, odd or neither g(x) = x* – 2x²

A:

Q: What is meant by a real function in reference to algebra?

A:

Q: Determine if the function is even, odd or neither f(x) = x4 - x2 + 2

A: We plug -x in place of x and find f(-x) and simplify.

Q: Determine whether the function is one-to-one. f(x) = 3x - 2

A: Given the function f(x)=3x-2

Q: he weight, in pounds, of a baby in the first six months of life can be modeled by the function…

A: f(x)=1.5x+7, where x is in age in months.

Q: Differentiate the function.   f(x)  =240

A: We have to differentiate the function: fx=240 We know that differentiation of any constant is zero.…

Q: Give the range of the function in interval notation f(x) =2(x+1)2 + 7

A:

Q: Differentiate the function with respect to the independent variable. f(x) = 6 – 5x - 8x? f'(x) =O

A:

Q: Use a graphing calculator to find the value of f(x) when x =1 for the function f(x) =x2-1.

A:

Q: Determine whether it is even, odd or neither function  f(x)=4-5x

A: We have to find odd, even or neither for the given function: fx=4-5x We know that for the following…

Differential Equations

Have you ever observed the movement of the satellites and rockets or how the planets go around the sun in their orbits? How will you determine their motion? Definitely they follow some scientific laws and these kinds of problems are framed as differential equations.