Question

What is the domain and range for the following function and its inverse? f(x) = -x + 5

Answer 1

Answer:

The domain of linear function is always the set of all real numbers

Range is also the set of all real numbers

$f^{-1}=-x+5$

Step-by-step explanation:

$f(x) = -x + 5$

Domain is the set of x value and range is the set of y value. There is no restriction for x  and y in a linear function.

The domain of linear function is always the set of all real numbers

Range is also the set of all real numbers

Now find the inverse

$f(x) = -x + 5$

Replace f(x) with y

$y = -x + 5$

Replace x with y and y with x

$x = -y + 5$

Subtract 5 from both sides

$x-5=-y$

Divide both sides by -1

$y=-x+5$

Replace y by f^-1

$f^{-1}=-x+5$

Answer 2

Answer:

Domain: $\mathbb{R}$

Inverse: $f^{-1}(x) = -x + 5$

Step-by-step explanation:

Since this is a linear function, the domain and range is simply the set of real numbers.

The inverse is obtain by switching the places of x and y, then solving for y.

Here,

y = -x + 5

So switching x and y,

x = -y + 5

Solving for y again,

y = -x + 5

Thus,

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