Question

Is there anyone that could please help me with this question im struggling please

Answer 1

`\begin{cases} s(x)=x+2\\ t(x)=4x+3 \end{cases} \\\\[-0.35em] ~\dotfill\\\\ (s+t)(x)\implies s(x)+t(x)\implies \stackrel{s(x)}{x+2}~~ + ~~\stackrel{t(x)}{4x+3}\implies 5x+5 \\\\[-0.35em] ~\dotfill\\\\ (s-t)(x)\implies s(x)-t(x)\implies \stackrel{s(x)}{x+2}~~ - ~~\stackrel{t(x)}{(4x+3)} \\\\\\ x+2~~ - ~~4x-3\implies -3x-1 \\\\[-0.35em] ~\dotfill`

`(s\cdot t)(x)\implies s(x)\cdot t(x)\implies \stackrel{s(x)}{(x+2)}\stackrel{t(x)}{(4x+3)}\implies \begin{array}{llll} x+2\\ * ~~ 4x\\\cline{1-1} 4x^2+8x \end{array}~~ + ~~ \begin{array}{llll} x+2\\ * ~~ 3\\\cline{1-1} 3x+6 \end{array} \\\\\\ 4x^2+8x+3x+6\implies 4x^2+11x+6 \\\\[-0.35em] ~\dotfill\\\\ (s\cdot t)(4)\implies 4(\underset{x}{4})^2+11(\underset{x}{4})+6\implies 64+44+6\implies 114`