Question

what is the inverse of the function f(x)=x/5-2

Answer 1

Answer:

$\huge\boxed{\sf f^{-1}(x)=5x+10}$

Step-by-step explanation:

Given function:

$\displaystyle f(x)=\frac{x}{5} -2$

Put f(x) = y

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

Swap x and y

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

Now, solve for y

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

Add 2 to both sides

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

Multiply 5 to both sides

$5(x+2)=y$

Distribute

$5x + 10 =y$

Put y = f⁻¹(x)

$\boxed{f^{-1}(x)=5x+10}$

$\rule[225]{225}{2}$