Let f (x) = x2 +5 and g (x)= x-3 a. find the composite function of (fog) (x)  and simplify  b. find the value of fog (1)

Q: The function f is defined by f(x) = 2x +1. Find f(5x). f(5x) = 0

A: We can find f(5x) as below.

Q: Express the given function h(x) =1/(4x + 5) as a composition of two functions f and g so that h(x) =…

A: We need to express the above function h(x) as a composition of two functions f(x) and g(x) such…

Q: Let f(x) = { 3x² + 2, بی کر 2x - 3, if x < 3 if x ≥ 3 be a piecewise function. Evaluate 3 √₁³ f(x)…

A: It is known that: ∫xndx=xn+1n+1+C, where C is the integration constant.

Q: Evaluate the composite function, where f(x) = 2x + 3, and g(x) = x2 − 4x. (g ∘ f)(−1)

A:

Q: Express the given function h(x) = l3x - 4l as a composition of two functions f and g so that h(x) =…

A: Given :h(x) = 3x -4To express h(x) as a composition of two function f and g so that  h(x) = (f∘g)(x)…

Q: find the rules for the composite functions f o g and g 0 f  f(x) = 6x^2 + 3x +8  g(x) = x + 1

A: given: f(x)=6x2+3x+8g(x)=x+1

Q: Sketch the given function and find its domain and range 1 z = x² + y2

A: Consider a real valued function z=f(x,y) Then the domain of z = {(x,y): f(x,y) exists} and Range of…

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

A: Given:            fx=x+3  and  gx=x2-2

Q: Locate the discontinuities of the function. 2 f(x) = 1 + e7/x

A:

Q: Evaluate the piecewise function at the given values of the independent variable. 4x +3 if x< 0 f(x)…

A: Given piecewise function is  fx=4x+3       if x&lt;03x+6       if x≥0

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

A:

Q: Find the domain and sketch the graph of the function.

A:

Q: 15. Find the difference quotient f(x+h) – f(x) for the function f(x) = -x² + 2x +1. h

A: The given function is fx=-x2+2x+1To find difference quotient fx+h-fxh

Q: Evaluate the piecewise function at the given values of the independent variable. 5x +3 if x<0 f(x)…

A:

Q: Find the domain of a function of the form f (x) = va – x².

A: Given function:- f(x) =√(a-x2)  To find:- Domain of given function f(x)

Q: ,if x>2 Find the correct value of bb that makes

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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: B1(a): Find the value of k that makes function continuous at x = 4 3x + 6 x > 4 6x – k x < 4 f(x) =…

A:

Q: Evaluate the piecewise function at the given values of the independent variable. 2x + 3 if x<0 f(x)…

A: Given : fx = 2x+3   if x&lt;02x+7  if x≥0

Q: Consider the following function f(x)= - 3x2 + 5x – 2 where x€ (-x, +0). Find the following:

A: Here we have to find the inflection point of the curve f(x): inflection points fx=x33−3x2+5x−2

Q: A function f(x) is given as follows: 2x +1 f(x) = 3x - 1 f-(1) =?

A:

Q: Find a function f(x) such that f'(x) = 4e" – 3x and f(0) = 4 f(x) =

A:

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: Find the linearization L(x) of the function at a. f(x) = x3 − x2 + 9,    a = −2 L(x) = ?

A:

Q: find functions f and g so that f ∘ g = H.

A: A function defines a relationship between two sets, where one set is dependent on other set. Any…

Q: Find the most general function F such that F'(x) – 14. x5 || - F(x) = Σ

A:

Q: Calculate the output for the function with he given input. If there is no possible output for the…

A: The given function isfx=xx-1. Here function fx is not defined if x-1=0. x-1=0x=1 So, the function is…

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: The function h(x) ==x-1 represents the composite h(x) = f(g(x)). If f(x) = 2x – 1, what is g(x)?

A: Please refer the attached image for complete solution. Given : hx=43x-1, hx=fgxfx=2x-1To calculate :…

Q: Find a value for the constant k, if possible, that will make the function continuous. Skx², (2x + k,…

A: Answer: The solution is as given below:

Q: Consider the function f(x) = z + 6

A: Givenf(x)=1x+6

Q: Consider the function f(x) = 12x5 + 15x¹ - 240x³ +2. f(x) has inflection points at (reading from…

A:

Q: The domain for the function f(x) = V-2(x – 1) is

A:

Q: Express h(x) as a composition of two functions: h(x) = √(x2 + 5)

A:

Q: 2 V1-x*

A:

Q: Differentiate the following function. f(x) = 2e2x f(x) = 2 e (2e2x) =]

A: Given: fx=2e2x We know that ddxekx=kekx                                                          ..1

Q: Express the given function h(x) = (3x - 1)4 as a composition of two functions f and g so that h(x) =…

A: Given function,  h(x) = (3x - 1)4 To express the function h(x) as a composition of two functions f…

Q: find the value of the constant (a, b, or c) that makes the function continuous

A:

Q: The function h(x) 1 can be expressed in the form f(g(x)) where g(x) = (x + 7) and f(x) is x + 7…

A: Given ,  The function h(x) = 1/(x+7) can be express es in the form f(g(x)) where g(x) = (x + 7)  We…

Q: Find f(x) for the function. X x + 1 f(x) = f-1(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: Determine the value of x of the discontinuous function: * x – 1 x 3

A:

Q: Let h(x)=f(x)g(x). If f(x)=2x2+1,g(1)=0, and g′(1)=−1, what is h′(1)?

A:

Q: B1(a): Find the value of k that makes function continuous at x = 4 4x + 6 x > 4 f(x) = 6x – k x < 4…

A:

Q: Evaluate the piecewise function at the givern values of the independent variable 5x+3 if x<0 f(X) =…

A:

Q: Express the function h(x) = (x2 + 2x - 1)4 as a composition of two functions f and g so that h(x) =…

A: To express  function h(x) = (x2 + 2x - 1)4 as a composition of two functions f and g so that h(x) =…

Q: Express the function h(x)=1x+8h(x)=1x+8 in the form f∘gf∘g. If g(x)=(x+8)g(x)=(x+8), find the…

A: The given function is h(x) = x + 8.We have to express it as a composition of two functions f(x) and…

Q: 2. Let f be the function defined by 9) f (x) = x²+2x+1 ,Find: -f (3) +fヒ3)

A: