Let f(x) = { 3, 1< x < 2 0, 2 < a <5 and Let F(x) = { 3x, 1

Q: Sh -4*| [x* - 2x] ,15x<2 ,0<x<1 Let f(x) = Then discuss the differentiability of f(x)in(0,2).Here []…

A: The given function is: f(x)=1-4x2   0≤x&lt;1x2-2x1≤x&lt;2

Q: Prove algebraic ally that any function of the form f(x)=ax2n+4 (where n is an integer) is symmetric…

A: The given function is fx=ax2x+4. To prove fx=ax2x+4 is symmetric to the y-axis, it is enough to…

Q: 2x - 3x + 13x+a if x#2 f(x) = . X-2 b if x = 2

A: Solution:- It is give that f(x) is continuous at x=2  and the given function is  f(x)=…

Q: 4. Let the function f: R - {2} → R be defined by f(x) x-5 2x - 3 Prove that ran(f) = R-{}}.

A: The given problem is to prove that the range of given function is Ran(f)=R-{1/2} . Given function…

Q: Let f be a differentiable function such that 2 < f'(x) < 4 for all values of x. Show that 10 < f(12)…

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Q: Prove that the function f(x)=x^2 defined on the domain of all real numbers does not satisfy a…

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Q: ,for x 1 Discuss the contuniuty of f andf'.

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Q: Make a table of values that shows the function values of f(x)=x²-1 together with those of g(x)=3*…

A: f(x)=x2-1g(x)=3x

Q: If f (x) = x² - x and g(x)=√x-2, what is (fog)(x) ? Simplify your answer. x²-x-2 /x² - 2 2-x-2 O…

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Q: Q3) Test the continuity of the function f(x): -15x <0 0S X< 2 F(x) = 2х— 1 x+ 3 X = 2

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Q: (x2+3). Explain why √x4+24 Q7. Consider the function f : [0, 1] → R, x→ (a) f continuous, (b) f is…

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Q: Determine f,(x); f(x) = x2*, x > o

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Q: 58. Show that if f is a function and z = x+h, then f(2) – f(x) _ f(x+ h) – f(x) Z - x h

A: This question is taken from the function in which we have to prove the given equation. We can write…

Q: Let a and b be real numbers. Consider the function y = f(x) = 1x² ax+b For which values of a and b,…

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Q: t) For each of the following functions, state whether they are one-to-one or not. (You must enter T…

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Q: Define f(x) = {x2 if x ≤ 2                        5x > 2}  Find each of the following.  a) f(1) b)…

A: Function is given, if x is greater than or equal to 2 then the definition of the function is f(x)=x²…