inverse of y=x/5-2 — step-by-step solution

We have

y = \frac{x}{5} - 2

. The slope

\frac{1}{5}

is nonzero: the function is bijective on ℝ

⇥Let's solve in

ℝ

y = \frac{x}{5} - 2

⇥ⓘ We add

2

to both sides

⇥

y + 2 = \frac{x}{5}

⇥ⓘ We multiply both sides by

5

⇥

5 \cdot (y + 2) = x

⇥

x = 5 \cdot (y + 2)

⇥ⓘ Expand by multiplying each term inside the parentheses

⇥

x = 5 y + 5 \cdot 2

⇥ⓘ Multiplications are done before additions and subtractions:

5 \cdot 2

10

⇥Solution obtained:

x = 5 y + 10

▶Renaming the output variable

y

x

, the inverse function is

5 x + 10

, defined on ℝ