# Tagged Questions

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### Finding a formula using two other functions.

I am trying to find a formula for $p(x)$, but I am not seeing where to start. I have two functions $m(x)=9*27^x$ and $n(x)=9^x$ I need to find the formula for function $p(x)$ if $m(x) = p(n(x))$ ...
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### The limit of a composite function

I am presented with the following task: "You are given that $k(h) \neq 0$ and $h \neq 0$. If $\lim_{k \to 0} F(k) = L$ and $\lim_{h \to 0} k(h) = 0$, show that $\lim_{h \to 0}F(k(h)) = L$. This is ...
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### Left Inverse: An Analysis on Injectivity

I'm told that $g$ is a left inverse of $f$ if $g\circ f=1_X$. I'm also told that if $f$ has a left inverse, then $f$ must be injective. I'm now asked to prove the converse, namely that if ...
Suppose $F(x)=f(g(x))$ $g(1)=3$ $g'(1)=4$ $f'(1)=6$ $f'(3)=5$ What is $F'(1)$ ?
If $f: \mathbb{R} \to \mathbb{R}$ is continuous, and $\forall x \in \mathbb{R} :\;(f \circ f \circ f)(x) = x$, show that $f(x) = x$. The condition that $f$ is continuous on $\mathbb{R}$ is ...