3 (5) For the functions f(x) = and g(x) =+ 4, find f(g(x)) and g(f(x)), hence or X-4 otherwise determine whether g(x) is the inverse of f(x).

Q: 1 If f(x) = xī, then f'(x) is equal to %3D

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Q: 1. Find the domain and range of the inverse of f(x) = x – 6x +5 with domain restriction {x € R| 0<x<…

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Q: 2 show that (fof) (x) = x, for all x # 3 (4x + 3) Question 4. If f(x) = (бх — 4)" 3' What is the…

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Q: 15. With f(x) = 3x +1 and h(r) = 2x – 4, find (f oh)(5) - %3D

A: we know that  (fog)(x) = f (g(x))

Q: Graph the function f(x) = u₂(x) ln x + u5(x) (ln(10 − x) – In x) -

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Q: Let h(x)=f(x)g(x) where f(x)=−4x^2−5x+1, g(1)=−5, and g′(1)=−4 what is h′(1)?

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Q: Compute f'(x) a.) f(x) = (x2+1)e-x^2 b.) f(x) = (4e-x-

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Q: Let h(x) = f(z) where f(x) = ln(3x² + 2x +2) and g(x) = -2x. What is h' (x)?

A: hx=fxgx=ln3x2+2x+2-2xf(x)=ln3x2+2x+2 Differentiate f with respect to x…

Q: Let h(x)=f(x)g(x). If f(x)=x2−3x,g(0)=−1, and g′(0)=−4, what is h′(0)?

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Q: Consider the functions f(x) = x² – 5x + 4, g(x) = x² + 5x + 6 and h(x) = x² + x f(x) g((x) 3 h(x) a)…

A: We can solve this using definition of function

Q: The function h(x)= 1 over x-8, can be expressed in the form f(g(x)), where g(x)= (x-8) , and f(x))…

A: use composition of function to find the function f(x).

Q: Show that g(x) = x/(x-1) is equal to its inverse on the domain x-1 {x : x # l}.

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Q: 1, Differentiate the function. (2) f(x)= 5x² – x+1 (3) f(x)= (2+3x'j - nx (4) f(x)= e (5) f(x)= (x³…

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Q: Find for f'(x) | f(x) = x – cos(x) f(x) = e* – 2x - 2

A: To find f'(x).

Q: 2. Find the inverse of f(x) = 2x+1, r >0. %3D A. x +1 f(x) = V B. f(x) = Va +1 2 C. 1 -- f(x) = V D.…

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Q: The function f(x) = 2x^3 - 27x^2 + 108x - 4 has two critical numbers. The smaller one is x = ? And…

A: Hereupon plotting we can see that horizontal tangent can be drawn at points x=3 and x=6.  Note: The…

Q: Let h(x)=f(x)g(x). If f(x)=ln(3x2−2x−4) and g(x)=3x−1, what is h′(x)?

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Q: Verify if  F(x)=ln x -2x^3+5x^4 is an antiderivative of the function f(x)=(1/x)-6x^2+20x^3

A: Given, A function f(x) We have to verify that F(x) is the antiderivative of function f(x).

Q: Consider x2 2x + 1 if x 1.

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Q: 4. Given xo < x, and x, define x - xo X1 - X0 and let P1(x) interpolate the function f(x) at the…

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Q: If f(x) =3 ln x and g(x) = e2 , find go f(x). %3D

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Q: 9. If f(x) = kx – 1 and f'(15) = 2, find k. %3D -

A: Given f(x)= kx3 - 1 and f-1(15)=2 then we have to find out the value of k

Q: Let h(x)=f(x)g(x). If f(x)=−2x^2+2x+3 and g(x)=−x^2−3x−4, what is h′(−1)?

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Q: Suppose that f(x) I + 6 is differentiable and has an inverse for æ > 1 and f (2) = 8. Find (f ')'…

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Q: Consider x2 – 2x + 1 if x 1.

A: Given: f(x) = x2-2x+1        if x&lt;-1xx+1               if  -1≤x≤0x-1             if  0&lt;x&lt;10…

Q: Let h(x)=f(x)g(x). If f(x)=4x^2+3x+1 and g(x)=3x^2−3x−4, what is h′(−1)?

A: Given: hx=fxgx, fx=4x2+3x+1, gx=3x2-3x-4

Q: Let h(x)=f(x)/g(x), where f(x)=ln(3x2 +2x+2) and g(x)=−2x. What is h′(x)?

A: Here we use quotient rule, which is pq'=p'q-pq'q2

Q: let f(x) = (6x+3) and g(x)=(-2x+5) *use chain rule to calculate h'(x) where h(x)=f(g(x)

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Q: 21. Suppose f(x) = G and g(x) = v2**. Find the x-value for which the two functions are equal.

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Q: Differentiate the following function.   f(x)=9−2x+e−5x d/dx9−2x+e−5x=nothing   Enter your answer in…

A: fx=9-2x+e-5x

Q: 4. Prove that the following functions f (x) = Vx – 2 and g(x) = x² + 2 are inverses of each other…

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Q: FIND: hf(x)dx 2 g(x) dx = = f₁₁ f(x) dx = = if g(x) is an odd function. if f(x) is an odd function.

A: We need to find integral.

Q: 1. Evaluate the following functions at x = 7 a. f (x) - -18x -19 b. g (x) =-9x2 + 28x - 24 C. h (x)…

A: (1).  We have to evaluate the value of the given function at x = 7.

Q: Explain why g(x) = f(x), if x ≤2 0, if x > 2 is not differentiable at x = 2.

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Q: f(x) = 27x² + 3x5 - 24x³ + √2x f(x) = + √2x 3 x x5

A: Find the general anti-derivative F(x) + C for the following problem:

Q: 1/ Find the domain of the following functions : 1 1) f(x, y) = x²+y²+z²+16 2) f(x,y) = In(9 - x² –…

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Q: If f(x) = 3x – 2 and g(x) = x + 1, then (f(g))-'() equals O 1– x O x +1 O x – 1 1 O (3x – 1) 3

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Q: Suppose F(2) = 1, F(8) = − 1, and F'(x) = f(x). - 10 [ f(x) dz = 10

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Q: Find the linear inverse algebraically. (1 Point) f (x) = 3x – 4 O f-l f-l (x) = x-4 3 O f-l (x) =…

A: Given that, f(x) = 3x - 4 We have to find the linear inverse of given function f(x).

Q: 1) A course repeater claims that his brother who did some Calculus at college years ago, but…

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Q: Suppose that y =fx) = x2 – 4x +4. Then on any interval where the inverse function y= f(x) exists,…

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Q: course repeater claims that his brother who did some Calculus at college years ago, but currently on…

A: Given: fx=2x2-1x2+3x2+1 gx=x2+872-3x25 The objective is to check given first order derivative of…

Q: 6) Find the value of c such that {0, c} is 2-cycle such that c be a constant and let the function be…

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Q: ) Differentiate:  (a) f(x) = √x(cos)x2 (b) f(x) = 2x/x2 + 4

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Q: For j(x)=3*-¹, find j(x+h)-j(x) h 3x-1(3h) h 3x-1(3-1) h 3x-1(3+1) h ○(x-1)(3+1) h

A: Topic = Functions

Q: Find a simple function g(x) such that f(x) is O(g(x)), where f (x) = (-5x20 + 3)(-3x² – 4x²) + 7(4x²…

A: Given, f(x)=-5x20+3-3x7-4x2+74x2-2.3xx6+4 In In x Therefore,   g(x) is also a function…

Q: If f(æ) = (x + 1)² – 1 then f(1) – f(0) is equal to:

A: Given f(x)=(x+1)2-1 Now we will find the value of f(1)-f(0) as shown below

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.