30. Let f: RR and g: R → R be defined by f(x) = 3x + 1 and g(x) = x² - 2. Determine (fog)(2) and (gof)(2).

Q: Let f: Z → Z where f(x) go f(0) = fog(-3) = go f(x) = fog(x) = = x² + 6. Let g: Z → Z where g(x) = x…

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Q: 5. Let f(x) = x² + 3x and g(x) = 2-x. (a) Find (f - g)(x) (b) Find (fg)(2) (c) Find (4) (x) and its…

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Q: If f : R → R is defined by                      f(x) = x2– 3x + 2, find f (f(x)).

A: Given,

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: 3. Find [g f](x) for f(a) = 2x +5 g(2) = 2 – 3. and

A:

Q: 1. Let f(x) = x? – 1 and g(x) = x² +x – 6. (a) Find (f – 9)(x) (b) Find (x) and give its domain. (c)…

A: R is the set of all real numbers

Q: 4. Find the zeros of f(x) = x² + x – 3.

A: We know that, for a quadratic function fx=ax2+bx+c, the zeros of of fx is given as x=-b±b2-4ac2a…

Q: If the function f: R→R be defined by f(x)=x² +5x+9,Find f'(8) = and f'(9).

A: The given function is fx=x2+5x+9

Q: 4. Evaluate the functionf(x) = x² + 1 and g(x) = x - 4. Find a. (fᵒg)(3) b. (gᵒf)(1)

A:

Q: Use the table to determine Df(g(x))) at x = 3. |1 2 3 4 f(x) 1 f(x) |3 -5 1 4 4 1 3 4 3 2 g(x) 2…

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Q: 5. For f(x) = 2x - 1 and g(x) = x² - 2x, find: (A) f(-2) + g(-1) (C) g(2) f(3) (B) f(0) g(4) f(3)…

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Q: . Show that the function f: R→ R defined as f(x) = 13x − 15 is one-to-one.

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Q: xercise II.2. let F(): R² R³ and G(): R² R² be given by (fi(x)) f2(x) f3(x)) F(x) = (iii) f3 and ere…

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Q: 4. Let f-(x) = g(x) = x-5, k-1(10) + 7 = 10 and h(x) = then find: b. Domain of h(x). c. (hof)(2). (Z…

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Q: Let f(x) = 2x +3, g(x) = x – 4, and h(x)= 4x – 1. Compute (h o go f)(3).

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Q: Let f(x) = 4x+3. Determine (fofo f)(x).

A: Given,          The function is fx=4x+3 .

Q: 26. Let f (x) = vx - 1 and g(x) = x² – 4. A. Find (fog)(x) and (gof)(x). B. Find all real values of…

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Q: Q: Let f: R→R be given by f(x)= x +3 Find (a){x: f(x)= 28} (b) The pre-image of 39 and 2 under f.

A:

Q: 4. For f(x) = x² – 3x, evaluate a) f(2) [2,3,3] c) the value of x when f(x) = 4 b) f(m + 1)

A: Given,              f(x)=x2-3x

Q: Let f(x) 1 and g(x) = 4x + 7. Then с — 3 - (f o g)(0) = (f o g)(x) =

A: Given:

Q: ain of f+g, f-g, fg and

A: As per the bartleby guidelines for more than three parts only three has to be solved. Please upload…

Q: 3. Let f(x) = { ,x<2 ax + b, x22 Find a and b so that f (2) exists.

A: To find the value of a and b