Question

What is the domain and range for the following function and its inverse?

f(x) = -x + 5

f(x)
domain: all real numbers, range: all real numbers
f–1(x)
domain: all real numbers, range: all real numbers

f(x)
domain: x
`\geq 0`, range: y
`\geq 5`
f–1(x)
domain: x
`\geq 5`, range: y
`\geq 0`

f(x)
domain: x
`\geq 0`, range: y
`\geq 5`
f–1(x)
domain: x
`\geq 0`, range: y
`\geq 5`

f(x)
domain: x
`\leq 0`, range: y
`\geq 5`
f–1(x)
domain: x
`\geq 5`, range: y
`\leq 0`

Answer 1

"f(x)

domain: all real numbers, range: all real numbers

f–1(x)

domain: all real numbers, range: all real numbers"

Explanation:

We can use the fact that the domain of a function and the range of its inverse are equal.

Also, the range of the function and the domain of its inverse are equal as well.

Looking at the function f(x/ = -x + 5, we see that this is a line with a negative slope of 1 and a y-intercept of +5.

As we know from the graph of lines, there is no restricting values in x and y. So for the original function, domain is the set of all real numbers and the range is the set of all real numbers.

For the inverse, the range is set of all real numbers and domain is also the set of all real numbers.

First answer choice is right.