24 26 27 and 29 please Decide whether the composite function

Decide whether the composite functions, f g and g f, are equal to x. f(x) = x^2 + 2, g(x) = Squareroot x - 2 Yes, yes No, no Yes, no No, yes Use the properties of logarithms to find the exact value of the expression. Do not use a calculator. log_6 11 middot log_11 36 2 11 6 36 For the given functions f and g, find the requested function and state its domain. f(x) = 3x + 6; g(x) = 7x - 6 Find f middot g. (f g) (x) = 21x^2 + 24x - 36; all real numbers (f middot g)(x) = 21x^2 + 36x - 36; [x| x notequalto -36] (f g) (x) = 21 x^2 - 36; {x | x notequalto -36} (f g)(x) = 10x^2 + 24x + 0; all real numbers denotes the length of the are of a circle of radius r subtended by a central angle theta, find the missing quantity s = 1.65 meters, theta = 1.5 radians, r = ? 0.91m 0.4 m 0.55 m 1.1 m a polynomial whose zeros and degree are given. Zeros: 0, - 7, 6; degree 3 f(x) = x^3 + x^2 - 42 x for a = 1 f(x) = x^3 + x^2 + 42x for a = 1 Zeros: -5, multiplicity 2; 3, multiplicity 1; degree 3 x^3 - 7x^2 - 30x + 75 x^3 - 7x^2 - 5x + 75 x^3 + 10x^2 - 5x - 75 x^3 + 7x^2 - 5x - 75

Solution

24. f(x)=x²-2 , g(x)= sqrtx   - 2

fog(x)= f(g(x))= f(sqrtx - 2)= (sqrtx - 2)²-2= x+4-4sqrt x   - 2= x -4sqrtx+2

gof(x)= g(f(x))=g(x²-2)= sqrt(x² - 2) -2

So none of them equal to x

26.f(x)= 3x+6     g(x)=7x-6

f.g(x)= (3x+6)(7x-6)= 21x²+24x-36

Hence the correct option is a

27.   s=1.65 m

theta=1.5 radian

s= r* theta

1.65=1.5 r

r=1.65/1.5= 1.1 m