Proving composition of functions
11798
If $f \circ g$ is onto then $f$ is onto and if $f \circ g$ is one-to-one then $g$ is one-to-one
136996
Fourier transform of function composition
113065
Proving equivalences of statements equivalent to AC
97371
Proving a function is constant, under certain conditions?
24126
When functions commute under composition
14277
Proving $f(x)=x\cdot |x|$ is a bijection
13253
Prove $f(S \cup T) = f(S) \cup f(T)$
145785
Sets of functions closed within composition.
409
functions satisfying $f(x - y) = f(x) f(y) - f(a - x) f(a + y)$ and $f(0)=1$
130023
Prove that the sum of two continuous functions is continuous
58988
Composition of convex function and affine function
96202
Prove composition of bijections is bijection
42579
Composition of 2 involutions
34836
Composition of Absolutely Continuous Functions
152438
Is the composition of two injective functions injective?
45710
Finishing a proof: $f$ is injective if and only if it has a left inverse
125682
Proof verification: the product of two continuous functions is continuous