Let f(x) and g(x) be functions. Prove, using contradiction method, that if f(g(x)) is one-to-one, then g(x) is one-to-one.That is, suppose that g(x) were not one-to-one and derive that f(g(x)) cannot be one-to-one.

Q: Evaluate  f(−7), f(0), and f(3)  for the piecewise defined function. f(x) =    x + 2     if x < 0…

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Q: Let f(x) = m1x + a and g(x) = m2x + b, where m1, m2, a, and b are constants. Determine the necessary…

A: f∘g=g∘ffgx=gfxfm2x+b=gm1x+am1m2x+b+a=m2m1x+a+bm1m2x+m1b+a=m1m2x+m2a+bm1b-b=m2a-abm1-1=am2-1

Q: et f and g be two functions. Given that (f o g)(x) =(x+1)/2 and g(x) = 2x-1, find f(x-3)

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Q: Let ƒ(x) = 2x2 + 5x and g(x) = 4x + 1. Find g[f(x)]

A: Given: fx=2x2+5x . gx=4x+1 . gfx can be calculated by replacing the x by fx in the function gx as,…

Q: a. Determine whether f(x) = 5/(x+1) is a one-to-one function from R to R, if not, give a counter…

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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: Suppose f is a real function satisfying f(x + f(x)) = 4ƒ(x) and ƒ(1) = 4. What is ƒ(21)? f(21)=

A: Suppose f is a real function satisfying f(x+ f(x))= 4f(x) and f(1) = 4, what is f(21)?

Q: Let f : R → R, where f(n) = 5 . Answer the following questions. 7x²+3*

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Q: Let f1(x) and f2(x) be functions from the set of real numbers to the set of positive real numbers.…

A: Big-O Notation:Definition: Let f and g be functions from the set of integers or the set of real…

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: f(x) – 10 • lim I – 1 = 6; • lim[g(x) + 2] = 5; • 3x < h(x) <r* + 2, for every x close to

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Rate of Change

The relation between two quantities which displays how much greater one quantity is than another is called ratio.

Slope

The change in the vertical distances is known as the rise and the change in the horizontal distances is known as the run. So, the rise divided by run is nothing but a slope value. It is calculated with simple algebraic equations as: