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

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

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):
$$\displaystyle{{f}^{{-{{1}}}}{\left({x}\right)}}=\frac{{1}}{{3}}{x}+\frac{{5}}{{3}}$$

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Previous studies show that $$\sigma_1 = 19$$.
For Englewood (a suburb of Denver), a random sample of $$n_2 = 12$$ winter days gave a sample mean pollution index of $$x_2 = 37$$.
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