Question

Look at the function f(x) = −x + 5. Which of the following describes the domain and range of the function and its inverse?

Answer 1

Domain of this function become R

Explanation:

Answer 2

The inverse is g(x)=-x+5.

Both f and g have domain and range all real numbers.

In interval notation that is
`(-\infty,\infty)`

Explanation:

f(x)=-x+5 is a linear function.

Since isn't f(x)=constant then it is diagonal so this means the range is all real numbers.

For any linear function, the domain will be all real numbers.

So to find the inverse of y=-x+5, you interchange x and y and resolve for y.

y=-x+5

(interchange)

x=-y+5

(solve for y)

Subtract 5 on both sides:

x-5=-y

Multiplying both sides by -1:

-x+5=y

So the inverse is g(x)=-x+5. To find find the domain and range of the inverse function given you already did it for the original function, the sets are swapped. The sets were the same here because they were both all real numbers.