Use the definition of a one–to–one function to determine if the function is one–to–one. h (x) = x2 + 3 =

Q: In the given equation , identify a function f that has the given characteristics. Then sketch the…

A: Givenf(0)=2f'(x)=-3 for -α<x<αTo find f

Q: Determine algebraically whether the given function is even, odd, or neither. 8x h(x) 3D 7x +5

A: hx=8x7x2+5 The given function is rational function. If the given function gives the same function…

Q: Evaluate the function ( f/g)(0) for f(x) = x + 3 and g(x) = x2 − 2.

A: Given functions are fx=x+3 and gx=x2-2.   The objective is to find f/g0.   It is found by…

Q: Find the domain of the function. (If you need to use -o or co, enter -INFINITY or INFINITY.) f (x) =…

A: Given: fx=3-12x     if x≤29x-4       if x>2 To Find: The domain of the function

Q: determine (algebraically) whether the given function is even, odd, or neither.   G1x2 = 1 - x + x3

A: Given equation: Gx=1-x+x3

Q: determine algebraically if the function is odd, even, or neither. g(x) = -2x4+ x

A: use the definition of even funtion or odd function.

Q: Express the function h(x)=(x+8)8 in the form f∘g. If f(x)=x8, find the function g(x).

A: Given,

Q: Evaluate the piecewise function at the given values of the independent variable. x+5 g(x) = if x2 -…

A: Given:

Q: Differentiate the expression with respect to x, assuming that y is implicitly a function of x. ( x2…

A: It is given that y is implicitly a function of x. =x2+y23/2 differentiate with respect to x

Q: determine (algebraically) whether the given function is even, odd, or neither.   f1x2 = x1 + x2

A: fx=x1+x2 A function f is said to be an even function if f-x=fx and an odd function if f-x=-fx.

Q: Consider the following function. g(x) = x2⁄3 If a ≠ 0, find g′(a).

A:

Q: Determine if the function is even, odd, or neither:  f(x)=(√(x^6))+(1/x)

A: Given the function A function f(x) is called an even function if for every input x, A function…

Q: Can a function such as f (x) = 53x be written in the form f (x) = bx? If so, what is b?

A: Comparison of the functions helps to determine the validity of the statement. The given function is…

Q: Evaluate piecewise function at the given values of the independent variable.

A: gx=x+3        if  x≥-3-x+3   if x<-3 a). g0=0+3         Because, gx=x+3   if  x≥-3 and 0>-3=3…

Q: Determine algebraically whether the function is odd, even, or neither. F(x)= x^2 -4x+6

A:

Q: Evaluate the function ( f − g)(1) for f(x) = x + 3 and g(x) = x2 − 2.

A: To Evaluate the function ( f − g)(1). Given that the functions are f(x) = x + 3 and g(x) = x2 − 2.

Q: Express the function in the form f ∘ g.

A: To express the function in the form of (fog). G(x)=1x+3 Solution: Given,G(x)=1x+3 We know,…

Q: Determine f (x) for each of the given function. f (x) = 2x 3 -

A: SOLUTION-

Q: Which of the following functions passes through the point(0, 10) and satisfiesf'(x)= 87

A: given f'(x)=8

Q: Evaluate the piecewise function at the given values of the independent variable. x+5 if x2 - 5 g(x)…

A: The objective of the question is  to evaluate the value of the given piecewise function at given…

Q: Determine the new value of the function f(x) =x+ Inx if the independent changes from x=2e to x=2.2e

A: Given f(x) = x + ln(x)Value of function at x = 2ef(2e) = 2e + ln(2e) = 2e+1+ln2

Q: Classify all the functions as either even, odd, or neither. 1. f (x)=x²+x*-x°

A: To classify a function f(x) as either even, odd or neither, we substitute -x in place of x and check…

Q: For Exercise, determine if the function is even, odd, or neither. -x v(x) x| + 2

A:

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

A: Given function, hx=x2+x.   The objective is to determine that whether the given function is  even,…

Q: The functionh is defined as follows. x-7 h(x) = x+12 Find h (-1).

A: hx=x-7x+12substitute x=-1h-1=-1-71-+12           =-811

Q: Evaluate the function ( f + g)(−1) for f(x) = x + 3 and g(x) = x2 − 2.

A: For two functions f and g, we have, f+gx=f(x)+g(x)

Q: Express the function h(x)=1x−9h in the form f∘g. If g(x)=(x−9), find the function f(x).

A: Topic = Functions

Q: Express the function h(x)=1/x+7h in the form f∘g. If g(x)=(x+7), find the function f(x).

A:

Q: If (-3, 1) is in the function f(x), then which of the following points will be in the function f…

A: (-3, 1) is in f(x)  Hence,  f(-3)  =  1    Taking the inverse of f at both sides    f-1 ( f(-3) )  =…

Q: Which of the following functions are 0(x²)? (Choose all that apply)

A:

Q: Find f(x+h)-f(x) given the following function.f(x) =-9x2-2x

A: f(x) = -9x2 - 2x Hence, f(x + h) = -9(x + h)2 - 2(x + h) = -9(x2 + 2hx + h2) - 2(x + h)

Q: Express the function in the form f ∘ g.

A: Given,  Fx=x-95   Since the formula for F says to first subtract 9 and then take the power of 5, we…

Q: Refer to the function f(x)=[x] determine f(-4.1)

A: Greatest integer function

Q: Use the functions below to find the given value f(x) = ±x - ( - 3 g(x) = x3

A:

Q: For Exercise, determine if the function is even, odd, or neither. f(x) = 3(x – 4)?

A: Given function

Q: 2. f (x)= |x | + 6

A:

Q: Evaluate piecewise function at the given values of the independent variable.

A: hx=x2-9x-3   if  x≠3    6       if  x=3 a). h5=52-95-3    ∵hx=x2-9x-3 if x≠3, here 5≠3=8 b).…

Q: Evaluate the piecewise function at the given values of the independent variable. x+4 if x2 -4 g(x) =…

A:

Q: Decide if the function is odd, even, or neither using definition f(x) 22 3x

A: Refer to the question.To check whether the function is even if f(-x) =f(x) for all real value of x…

Q: Differentiate the function. h(x) = 11 csch- (x³ ) Give your answer in exact form. W (x) =

A:

Q: Express the function h(x)=1x+7 in the form f∘g. If g(x)=(x+7), find the function f(x)

A: Given,

Q: Assume that f is a one-to-one function. If g(x) = x2 + 4 with x ≥ -2, find g-1(5).

A: One-one function takes unique value of y for every unique x. g-1(x) is the inverse function gives,…

Q: Express the function,h(x) = (2x - 5)3 as a composition of two functions f and g so that h(x) = (f ∘…

A: Given, hx=2x-53

Q: Evaluate the piecewise function at the given values of the independent variable. if x2 - 5 x+5 g(x)…

A:

Q: Let f(x) = 2x - 1 and g(x) = x2 + x - 2. Find the function: (fg)(x)

A: It is given that, fx=2x-1  and  gx=x2+x-2 We have to find the function :fgx

Q: Evaluate the piecewise function at the given values of the independent variable. x+5 if x2 - 5 g(x)…

A: Given that, g(x) = (x + 5),       if  x > -5 g(x) = - (x + 5),    if x < -5 We have to find…

Transformation of Graphs

The word ‘transformation’ means modification. Transformation of the graph of a function is a process by which we modify or change the original graph and make a new graph.

Exponential Functions

The exponential function is a type of mathematical function which is used in real-world contexts. It helps to find out the exponential decay model or exponential growth model, in mathematical models. In this topic, we will understand descriptive rules, concepts, structures, graphs, interpreter series, work formulas, and examples of functions involving exponents.