1. Find all values of k for which the function r2 _ 52 – 6 - 2x - 4 is continuous at x = 2. f(x) = 2k²-k if x # 2, if x = 2

Q: 6. Let r(x) = 1 + 3r– 10 and s(x) = x- 2. Build a new function, 1(x), for which 1(x)=| State any…

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Q: Let f(x) = x + √2x3 + x. Verify whether f[0, 1, 2, 3, 4] = f [0, 1, л, е, -1].

A: The details solution of the given question is given below in step 2.

Q: A bucket has a leak that started 6 hours ago. At time 0, when the bucket just emptied, a tap was…

A: Which option represents  the amount of water in the second bucket.

Q: Suppose that the functions u and w are defined as follows. u (x) = - 5x-2 w (x) = -x+3 Find the…

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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 absolute maximum and absolute minimum of the function f(r) =r² - 8z+7 over [1, 8].

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Q: 2. Find (fo g)(x), (g o f)(x) and the domain of each new function. a. Let f (x) = 4x² – x + 10 g(x)…

A: Here, we have given some functions and we have to find composite function and domain of these…

Q: What type of discontinuity occurs at x = 1 for the piecewise function? if x <1 if 1<x 3+ x h(x) =…

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Q: Consider the piecewise function 1 3.x if x < -2 f (x) = ax2 + 2x + b if – 2 < x Where a and b are…

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Q: Show that the function x- 16 - f (x) = x + 4 4 - 10 x = 4 has a removable discontinuity at x = 4.

A: A real valued univariate function f=f(x) is said to have removable discontinuity at c in its domain…

Q: Determine the values of x for which the function f(x) = {2x2 − 4    x 5…

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Q: Draw the function of y = x 2 / 3 + x2

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Q: 4. Are the following functions cubic splines? a. f(x) - x- 2x + 3, 0 sxs 1, - 2x - 3x2 + x + 2, 1 s…

A: Given :(a) f(x)=x3-2x+3, 0≤x≤1             =2x3-3x2+x+2, 1≤x≤2(b) f(x)=5x3-3x2+1 0≤x≤1…

Q: Suppose f is a function that satisfies f(2) = 20 and f(2n) +nf(2) = f(2n + 2) for all positive…

A: It is given that, f(2)=20      ...(1) and  f(2n)+nf(2)=f(2n+2)     ...(2). Here, 'n' must be a…

Q: Suppose that the functions q and r are defined as follows. 2 q (x)=x² +5 r (x)=/x+7 Find the…

A: The given functions are qx=x2+5 and r(x)=x+7 Find r∘q(2) and q∘r(2) as follows.

Q: ƒ(x) = = ax² + 3x + b 9x² - 6x + 2a if x ≤ 0, if x > 0.

A: f(x)={ax2+3x+b if x≤09x2−bx+2a if x&gt;0