2. Which of the following are proper rational functions? 4 (b) 9 — х 4x3 — 7х х (a) x2 + 12 (х + 2)(х + 1)(х — 3) (d) (х — 3) (2х + 5)(9— х) (c)

Q: y² = 2x = x² 1- y² = (x - 1)² x = 1+√1-y²

A: (a-b)2 = a2 - 2 a b +b2

Q: ) Find the domain of (i) f (x) = 1+ x? (ii) 8(2)= /4 – z?

A: given function f(x) = 1+x2

Q: S (et +3e²x) dx 2x 5+4et-e²x

A:

Q: If f(x) 52-8 ²-8 f (4x) + 1 = for x + √8, what is ƒ (4x) + 1?

A:

Q: Given f (x) = 7-5x a] f-¹ (4) b] f¯¹ (-4) + f¯¹ (-3) + f¯¹ (-2) c] g (x) = f-¹ (2x) 1 determine

A: The given function .The objective is to find the following values,(a) (b) (c) .

Q: Use the functions given by f(x) = 53√x - 1 O 1253√x - 1 53√√x + 1 O 1253√√x + 1 05√√x + 1 ○ 1 125 x…

A: given  f(x)=1125x-1given  g(x)=x3

Q: (x+1)/(x-1) + 2 > 0

A: We need to find the interval of x for which the given inequality holds good.

Q: Let f(x) = 4+ (5x +9)³. Find f¹(x) = (1) · (√(x − 4) – 9) Find (ƒ(2)) -¹ = (¹) · (√(x-4) – 9)

A:

Q: Find f (x) for f(x)=-- O f-¹(x) = -5x2 O = f-¹(x) 2 5x+3 O f-¹(x)= 3x 2 O f-¹(x) = 5x-3 -2x 5x-3…

A:

Q: f(x) = xv3+ 2 (-2)

A: Given: fx=x3+x2

Q: f(a + h) – f(a) 7. If f(x) = 3x² +9, find and simplify where h + 0. h За + 6h 3h + 12a ба + 3h 3h +…

A: Hence option (c) is correct.

Q: If f(x)= 10x -37x+11, then there are two real numbers a<b such that fla)=f(b)=4, and there is a real…

A: Please see the answer below

Q: Let g(x)=x2+6x        and f(x)=4x       Find each of the following.      a)  g(−1)      b)…

A:

Q: rovided f(x) = the square root of x2 +3 and g(x)= x/x+6 find (f o g)(4) and (g o f) (4)

A:

Q: Given f(x) = 7 + 3  /  8  , then f-1 (x)  will be?

A:

Q: for f(x) = (x-1)3 and g(x) = 1 - 4x, find the following  a) (f o g)(x) b) (g o f)(x) c) f(f(x))…

A: (fog)(x) = f[g(x)].

Q: Find f(g(-5)), if f(x) = „4 and g(x) = (x+ 4)² O -7/9 O -7/3 O 2/9 O 1051/81

A:

Q: Let f(x) = 2x + 8, g(x) h(x) — 3х — 6. = x + 2x – 8,and Perform the indicated operation. (Simplify…

A: Given that fx=2x+8,gx=x2+2x-8 and hx=3x-6To find :f-gxSolution :f-gx=fx-gx=2x+8-x2+2x-8…

Q: Assume that the domain of f and f-1 is (-∞, ∞o). Solve the equation for x using the given…

A: Given that the domain of f and  is (a)  ; (b) ;

Q: Find f(a), f(a + h), and the difference quotient f(a + h) − f(a) h , where h ≠ 0. f(x) = 7 −…

A:

Q: (b)     (g ∘ f)(x)     (c)     f(f(x))

A: The objective is to find the required values

Q: Find all rational roots of f(x) = 3x3 − x2 + 15x− 5.

A: The objective of this question is to find all the rational roots of the given polynomial function…

Q: 5х -4 f(x) = 6x2 + 7x- 3 Part 1 of 3 5х -4 f(x) = will not be a real number when the denominator is…

A:

Q: Let  f(x) = (2x − 9) / (x + 2). (b) Show f −1 exists. Let f(a) = f(b) and show that a = b.…

A:

Q: Let f(x) = x - 6 and g(x) = 7x. Find (f+ g)(1). (f+ g)(1)= (Simplify your answer. Type an integer or…

A: As per the question we can solve it as per the rules of function

Q: 3. Compute and completely sin (a) f(x) = 7-x+2x²

A:

Q: If f(x) = 2x +2, g(x) = - 3x - 2x-2, and h(x) = 7x² +5, find f( - 3). f(- 3) =O (Simplify your…

A: Given: fx=2x+2, gx=-3x2-2x-2, hx=7x2+5 For finding value of f-3, we put x=-3 in given fx and…