I need to construct proofs of the following. Someone please help me. I can't afford to take this class again!

Question

5. prove that if f:A-->B with Rng(f) = C, and if f^-1 is a function, then f o f^-1 = I_c.
15. Prove or disprove
a)if f is a linear function with positive slope, f is increasing on R.
b)if f and g are decreasing functions on an interval I, then f o g is decreasing on I.
c)if f and g are decreasing functions on I, then f o g is increasing on I.
16. Give two different examples of
b)a pair of functions f and g s.t. (f o g)(x)=square root of (2x^2-5).
c)a pair of functions f and g s.t. (f o g)(x)=sin[abs. val](2x+4)
e)two quadratic functions f and g whose sum f + g is linear.

Answer 1

5. if y = f^-1 (x) then x = f(y)
and (f o f^-1) (x) = f(y) = x : f o f^-1 = I

15. a) f(x) = ax with a positive then
f(x2) - f(x1) = a(x2 - x1) : if x1 < x2 then x2 - x1 is positive and f(x2) - f(x1) too, f(x1) < f(x2)
f is increasing on R

b) false, if x1 < x2, then g(x1) > g(x2) then (fog)(x1) < (fog)(x2) : fog is increasing on I

c) true

16. b) g(x) = 2x² - 5 and f(x) = sqrt(x)
or g(x) = x² and f(x) = sqrt(2x - 5)

c) g(x) = 2x + 4 and f(x) = sin |x|
or g(x) = |2x+4| and f(x) = sin x

c) f(x) = x² + x and g(x) = - x²
or f(x) = 2x² +4x + 3 and g(x) = -2x² +7x - 3