Question

Find the inverse of the following function​

Answer 1

Answer:

ƒ^-1 (x) = $\frac{2-7x}{2+x}$

Step-by-step explanation:

Substitute y for f (x)

$y = \frac{-2x+2}{x+7}$

Interchange x and y

$x=\frac{-2y+2}{y+7}$

Swap the sides of the equation

$\frac{-2y+2}{y+7} = x$

Multiply both sides of the equation by y + 7

-2y + 2 = (y + 7)x

Distribute x through the parentheses

-2y + 2 = xy + 7x

Move the expression/constant to the left-hand side and change its sign

-2y - xy + 7x - 2

Factor out  from the expression

(-2 - x)y = 7x - 2

Divide both sides of the equation by -2 - x

$y = \frac{7x-2}{-2-x}$

Simplify the expression

$y = \frac{2-7x}{2+x}$

Substitute ƒ ^-1 (x) for y

$f^{-1} (x) = \frac{2-7x}{2+x}$

Answer 2

f-¹(x)=$\frac{2-7x}{x+2}$

Answer:

Solution given:

f(x)=$\frac{-2x+2}{x+7}$

Let f(x)=y

y=$\frac{-2x+2}{x+7}$

Interchanging role of x and y

x=$\frac{-2y+2}{y+7}$

doing crisscrossed multiplication

x(y+7)=-2y+2

now solve it:

xy+7x=-2y+2

keep like terms in one side

xy+2y=2-7x

take common

y(x+2)=2-7x

make a value of y

y=$\frac{2-7x}{x+2}$

So,

f-¹(x)=$\frac{2-7x}{x+2}$