7. f(x) = x + √√/2x - 3, 3 2 x - 3 x-2' 8. f(x) = g(x) = 3 g(x) = = 3 r2 – 5r+6

Q: show that 1f ∘ g2 (x) = 1g ∘ f2 (x) = x.

A: Given: fx=1x, gx=1x. To find: f o gx=g o fx=x Solution: Finding f o gx. f o gx=fgx=f1x=11x=x

Q: The sketch represents f(x) = x² + x – 6 and g(x) = -x – 3 P M

A: We have given functions  f(x) = x2+x-6  g(x) = -x-3 As we have given to solve for  f(x) < g(x)…

Q: Xx) = x2, g(x) = x-8

A:

Q: Find (a) the domain of  f and (b) f-1 and its domain.   f(x)  = In  (2 + In x)

A:

Q: Does f=g?

A:

Q: Let f(x) = 3x – 1 and g(x) = 4 - x. Find all values of x for which f(x) < -1 or g(x) < -2.

A: Consider the function f(x)=3x-1 and g(x)=4-x. To find all values of x for which f(x)&lt;-1 or…

Q: Assume that f(x) is one -to-one. Find f-1 f(x) = x3 -3 f-1(x) =

A:

Q: (f ·g)(x)= f(x) g(x) O True O False

A: we have given (f.g)(x)= f(x) . g(x)

Q: Determine F(x) if, for all real x and y, F(x)F(y) – F(xy) = x + y.   Hint:  What could F(1) be?

A: Consider the provided question, We have to find F(x).

Q: Let both f(x) and g(x) be odd functions. If possible, determine whether each function must be even…

A:

Q: 2 Let f(x)=Vx and g(x)=- x-4

A: Given that  f(x)=√x and g(x)=2/(x-4) To find the f of g

Q: Let f be a function of x. f (x) = (x – 3)4 is an even function. - O True O False

A: Solution: The objective is to determine whether the given function is even or not

Q: Consider the following functions. Rw) - st) - (a) Find (e g)(x). Find the domain of feg. OR- (0, 4)…

A: fx=xx-3, gx=4x

Q: Consider two functions f(x) and g(x), and such that fˆ−1 (x) = g(x) Must it also be true that…

A: To explain that if f-1x=gx then g-1x=fx is true or not.

Q: f(x) = x+1 x-3

A: Given:  fx=x+1x-3To prove: f(x) is 1-1 we know that, If f(x1) = f(x2) then x1 = x2 therefore f(x) is…