We have \displaystyle{f}:\mathbb{R}\to\mathbb{R},{f{{\left({x}\right)}}}={x}^{{2}}-{\left({m}-{1}\right)}{x}+{3}{m}-{4};{m}\in\mathbb{R}. Which are values of \displaystyle{m} for which \displaystyle{f{{\left({x}\right)}}}{<}{0},\forall{x}\in{\left({0},{1}\right)} ...

Let \displaystyle{f{{\left({x}\right)}}}={5}{x}-{4}{\quad\text{and}\quad}{g{{\left({x}\right)}}}={x}+{7} . Determine \displaystyle{\left(\text{d}\right)}{a}:{\left({f}\circ{g}\right)}{\left({x}\right)},{\left(\text{d}\right)}{b}:{\left({g}\circ{f}\right)}{\left({x}\right)},{\left(\text{d}\right)}{c}:{\left({f}\circ{g}\right)}{\left({3}\right)}{\left(\ldots\right)} ...

How do you verify if \displaystyle{f{{\left({x}\right)}}}={x}+{4};{g{{\left({x}\right)}}}={x}-{4} are inverse functions?

-60x+32=32x+-60

Let \displaystyle{f{{\left({x}\right)}}}={4}{x}+{5}{\quad\text{and}\quad}{g{{\left({x}\right)}}}={4}{x}{2}-{5} . What is \displaystyle{\left({f}\cdot{g}\right)}{\left({x}-{1}\right)} ?

If \displaystyle\text{}{{f}^{{2}}{\left({x}\right)}}+{{g}^{{2}}{\left({x}\right)}}+{h}^{{2}}{\left({x}\right)}\le{9} and \displaystyle{u}_{{x}}={3}{f{{\left({x}\right)}}}+{4}{g{{\left({x}\right)}}}+{10}{h}{\left({x}\right)} ...