For the functions f(x)=10x-8 \text{and} g(x)=5x+7, find the following. (a)(f+g)(x) (b)(f-g)(x)

boitshupoO 2021-09-06 Answered
For the functions \(\displaystyle{f{{\left({x}\right)}}}={10}{x}-{8}\text{and}{g{{\left({x}\right)}}}={5}{x}+{7}\), find the following.
\(\displaystyle{\left({a}\right)}{\left({f}+{g}\right)}{\left({x}\right)}\)
\(\displaystyle{\left({b}\right)}{\left({f}-{g}\right)}{\left({x}\right)}\)

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Expert Answer

Obiajulu
Answered 2021-09-07 Author has 24538 answers
Step 1
Let Given function \(\displaystyle{f{{\left({x}\right)}}}={10}{x}-{8}{\quad\text{and}\quad}{g{{\left({x}\right)}}}={5}{x}+{7}\)
\(\displaystyle{\left({a}\right)}{\left({f}+{9}\right)}{\left({x}\right)}\)
we know that, \(\displaystyle{\left({f}+{9}\right)}{\left({x}\right)}={f{{\left({x}\right)}}}+{9}{\left({x}\right)}\)
\(\displaystyle\Rightarrow{\left({f}+{9}\right)}{\left({x}\right)}={f{{\left({x}\right)}}}+{9}{\left({x}\right)}\)
\(\displaystyle={\left({10}{x}-{8}\right)}+{\left({5}{x}+{7}\right)}\)
\(\displaystyle{\left({f}+{9}\right)}{\left({x}\right)}={15}{x}-{1}\)
Step 2
\(\displaystyle{\left({b}\right)}{\left({f}-{9}\right)}{\left({x}\right)}\)
we know that, \(\displaystyle{\left({f}-{9}\right)}{\left({x}\right)}={f{{\left({x}\right)}}}-{9}{\left({x}\right)}\)
\(\displaystyle{\left({f}-{9}\right)}{\left({x}\right)}={f{{\left({x}\right)}}}-{9}{\left({x}\right)}\)
\(\displaystyle={\left({10}{x}-{8}\right)}-{\left({5}{x}+{7}\right)}\)
\(\displaystyle={10}{x}-{8}-{5}{x}-{7}\)
\(\displaystyle{\left({f}-{9}\right)}{\left({x}\right)}={5}{x}-{15}\)
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