Explain the steps you would take to find the inverse of f(x) = 3x − 4. Then find the inverse.

Explain the steps you would take to find the inverse of f(x) = 3x − 4. Then find the inverse.

Question
Functions
asked 2021-02-08
Explain the steps you would take to find the inverse of f(x) = 3x − 4. Then find the inverse.

Answers (1)

2021-02-09
Let y=f(x):
y=3x−4
Swap the variables:
x=3y−4
Solve for y. Add 4 to both sides:
x+5=3y
Multiply both sides by 1.3.
\(\displaystyle\frac{{1}}{{3}}{\left({x}+{5}\right)}=\frac{{1}}{{3}}{\left({3}{y}\right)}\)
\(\displaystyle\frac{{1}}{{3}}{x}+\frac{{5}}{{3}}={y}\)
or
\(\displaystyle{y}=\frac{{1}}{{3}}{x}+\frac{{5}}{{3}}\)
The new y is the inverse of f(x):
\(\displaystyle{{f}^{{-{{1}}}}{\left({x}\right)}}=\frac{{1}}{{3}}{x}+\frac{{5}}{{3}}\)
0

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