4. (i) If u, is a ratìonal function of second degree, prove that d b+c a + c a +b (a – b) (a – c) Ua + (b - c) (b- a) Uf + (c - a) (c – b) dx | x= 0 Hence evaluate Ea (b+ c) (b c)

Q: Find all the rational zeros of the function f(x) = 2x - 9x4 + 9x³ - 3x² + 7x + 6. -1, 2 x = 을 3,2 x…

A: Roots satisfyf(x)=0f(x)=2x5-9x4+9x3-3x2+7x+6f(-1)=-24f(1)=12Options, A and E ruled…

Q: 4. f (x) = 5 - x and (gof) (x) = x2-10x + 30 since the function g(x) is the following- which is…

A: The solution is:

Q: Use algebraic manipulation to prove that (X +Y)(X + Y) = X

A: Given: X+YX+Y=X Now, first we shall simplify left hand side of equation.

Q: Let f(x, y) = \/125 – 2x? – 3y? - Evaluate f(3, 2)

A:

Q: ) Is the function f(x) = differentiable on the open interval (-1,1)? x².

A:

Q: f(x) = 8+x 8 - x on [4, 6].

A:

Q: 6. Use algebra to determine whether the given functions are is even, odd or neither a) f(x) = -x³ +…

A: For a given function f(x)  If it satisfies the condition  f(-x) = f(x), then the function is Even.…

Q: If f (x) = x2 + 2x + 1, find f (x +1). O a) f (x + 1) = x² + 2x + 2 O b) ƒ (x + 1) = x² + 4x + 3 O…

A: Given f(x) = x2 + 2x + 1

Q: 1. The function f(z) factors to f() = (* + 2)(ar + bz + c). Find (a + 6+ c). S(z) = 3+3r-5x+2 (a) 5…

A:

Q: f (x) = x²ex3-I

A: Given:        f(x) = x2 ex3-1

Q: 7. Differentiate f(x) = (3x + x)² in three ways. When you have completed all three parts, show that…

A: Given that, fx=3x+x2

Q: 11) For the function f(x)x+3 a) Find f(1) and f(m +6) b) Find the domain

A: We have been given a function and we are supposed evaluate its value for the given value/expression…

Q: The domain of the function f(x)=√12+4x−x^2 is the closed interval [A,B] where A= and B=

A: Domain is the set of all values that can be taken by x so that the equation is defined.

Q: The domain of

A:

Q: 20) For the the function f(x) 5x-2, find f(4a+ 1) A) a-1 C) 9a-3 B) 20a - 1 E) 20a + 3 D) 9a – 1

A: Given that  f(x)=5x-2 Find f(4a+1)

Q: Use the Product Rule to differentiate f(r) = Vr(5r - r)

A:

Q: Let S be the part of the graph of the function x² + y² that lies above the disk x² + y² ≤ 4. What is…

A: The surface is the part of z=x2+y2:

Q: What are the roots of the function f(x) = x³ + x² − 7x -3? O 3, 1+√2, 1-√2 O -3,-1+√2, 1-√2 O 1, 3,…

A: Solution :-

Q: Find a,b to continue the function at x=3 if: x > 3) x = 3 x < f(x) = ax + b 2ab + 1 bx - a +3 3)

A:

Q: what should n be if f(x) = Xn defineof a polynomial function?

A:

Q: Find fof where f(x) = 3x 5 and f: R R. - O al f(f(x)) = 9x – 20 O b f(f(x)) 9г? — 30х -25 Oo f(f(x))…

A:

Q: PLS HELP ASAP ON ALL

A: Approach to solving the question:Please see attached photos for detailed solutions. Thank you.…

Q: Let fx)-1+x+x² and h = 0. (5+1)-(5)-(1)? (a) Does O Yes No Well done! (b) Find f(x + h). (c) Does…

A: We need to find function.