Show that if f is symmetric with respect to x = a, then g(x) = f (x + a) is even.

Q: Does f=g?

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Q: Assume that f(x) is one -to-one. Find f-1 f(x) = x3 -3 f-1(x) =

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Q: Use the Intermediate Value Theorem (1VT) to show that the function. f(x) = lex² - 11x-7 has a zero…

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Q: Find the value of c so that the function x² + cx if x 1 is continuous for all real numbers.

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Q: Express the function F in the form f ∘ g ∘ h. (Enter your answers as a comma-separated list. Use…

A: first we analysis to given question that how to find f, G, h then we compute F(x) function.

Q: Determine F(x) if, for all real x and y, F(x)F(y) – F(xy) = x + y.   Hint:  What could F(1) be?

A: Consider the provided question, We have to find F(x).

Q: Let f(x) f-¹(-2) = x + 3 x + 6

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Q: 2 Let f(x)=Vx and g(x)=- x-4

A: Given that  f(x)=√x and g(x)=2/(x-4) To find the f of g

Q: Let f:Z+ à Z+ be defined as f(x)=x3 a. Draw a graph of the function by calculating the values of…

A: Let f be a function, f: ℤ+ → ℤ+ Then f(x)=x3 a. Let x be a positive integers, that is x=0,1,2,3,..…

Q: Let f (x) = x2 − 2x. Determine a domain on which f−1 exists, and find a formula for f−1 for this…

A: The given function is

Q: Let h be a function with h1(10)=-12, and let g(x)=h(x2+1). Find g1(3).

A: Given:  h'10=-12, gx=hx2+1 Find:g'3 As,   gx=hx2+1 Using Composition of functions and the derivative…

Q: Let f(x)=x2, g(x)=2x+5, and h(x)=x2-1 a. h[f(-2)] b. f[g(x-1)]

A: Given that , fx=x2 gx=2x+5 hx=x2-1

Q: 2 Let f(x)= 3x - 4 and let g(x) = 2x + 1. Find the given value. fig(3)] f[g(3)] = (Type an integer…

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

A: Given:  fx=x+1x-3To prove: f(x) is 1-1 we know that, If f(x1) = f(x2) then x1 = x2 therefore f(x) is…

Q: Let f(x) = 1 and g(x) +4. Then (fo g)(æ) (go f)(x) =

A: (f o g)(x) = x/6 (g o f)(x) =(4x -10)/(x-4)

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.