query: Solving/Proving Composite Functions
positive_passages.docid: 89514
positive_passages.text: Show that if $g \circ f$ is injective, then so is $f$.
negative_passages.docid: 137920
negative_passages.text: Proving an equation with invertible matrices
negative_passages.docid: 107686
negative_passages.text: Proof that the gamma function is an extension of the factorial function
negative_passages.docid: 4178
negative_passages.text: Solve $f(x)f(2x^2) = f(2x^3+x)$
negative_passages.docid: 117254
negative_passages.text: Solving a implicit, recursive function
negative_passages.docid: 114603
negative_passages.text: Conditional Expectation of Composite Function
negative_passages.docid: 14975
negative_passages.text: Functions satisfying $f:\mathbb{N}\rightarrow\ \mathbb{N}$ and $f(f(n))+f(n+1)=n+2$
negative_passages.docid: 47212
negative_passages.text: Solving functional equation
negative_passages.docid: 87390
negative_passages.text: Laplace equation of composite function
negative_passages.docid: 43870
negative_passages.text: Explain why a composite function in which g(x) is any function, is applied to the output of any even function h(x) , f(x) is always even.
negative_passages.docid: 6680
negative_passages.text: Solve for all possible functions f: $|f(x)-f(y)|=2|x-y|$.
negative_passages.docid: 109942
negative_passages.text: Find continuous functions such that $f(x+y)+f(x-y)=2[f(x)+f(y)]$
negative_passages.docid: 73519
negative_passages.text: Determine all functions satisfying $f(x + f(x + y)) + f(xy) = x + f(x + y) +yf(x)$
negative_passages.docid: 21391
negative_passages.text: Proving Functions are Surjective
negative_passages.docid: 75141
negative_passages.text: Quotient-Remainder Theorem Proving
negative_passages.docid: 90264
negative_passages.text: Combining pure functions
negative_passages.docid: 24810
negative_passages.text: Functions satisfying $(b-a)f'(\tfrac{a+b}{2}) = f(b)- f(a)$