f(x)=3x-1 and g(x)=x-2. How to solve (f/g)(x)?

Bradley Collier

Bradley Collier

Answered question

2022-12-21

f(x)=3x−1 and g(x)=x−2. How to solve (fg)(x)?

Answer & Explanation

hachatpg9

hachatpg9

Beginner2022-12-22Added 14 answers

\(\displaystyle{f{{\left({x}\right)}}}={3}{x}-{1}\)
\(\displaystyle{g{{\left({x}\right)}}}={x}-{2}\)
\(\displaystyle{\left(\frac{{f}}{{g}}\right)}{\left({x}\right)}\) means to split an expression into \(\displaystyle{f{{\left({x}\right)}}}\) by the expression for \(\displaystyle{g{{\left({x}\right)}}}\).
\(\displaystyle{\left(\frac{{f}}{{g}}\right)}{\left({x}\right)}=\frac{{{3}{x}-{1}}}{{{x}-{2}}}\)
Set \(\displaystyle{\left(\frac{{f}}{{g}}\right)}{\left({x}\right)}\) equal to \(\displaystyle{0}\).
\(\displaystyle{0}=\frac{{{3}{x}-{1}}}{{{x}-{2}}}\)
Multiply both sides by \(\displaystyle{\left({x}-{2}\right)}\).
\(\displaystyle{0}{\left({x}-{2}\right)}=\frac{{{3}{x}-{1}}}{{\color{red}\cancel{{{\color{black}{{\left({x}-{2}\right)}}}}}}^{{1}}}\times{\color{red}\cancel{{{\color{black}{{\left({x}-{2}\right)}}}}}}^{{1}}\)
Simplify.
\(\displaystyle{0}={3}{x}-{1}\)
Switch sides.
\(\displaystyle{3}{x}-{1}={0}\)
Add \(\displaystyle{1}\) to both sides.
\(\displaystyle{3}{x}={1}\)
Divide both sides by \(\displaystyle{3}\).
\(\displaystyle{x}=\frac{{1}}{{3}}\)

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