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, range: y
f–1(x)
domain: x, range: y

f(x)
domain: x, range: y
f–1(x)
domain: x, range: y

f(x)
domain: x, range: y
f–1(x)
domain: x, range: y

"f(x)  

domain: all real numbers, range: all real numbers  

f–1(x)  

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

Step-by-step 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.

region b will make the inequalities y < 2x + 1 and y > -x - 2 true ⇒ answer a

step-by-step explanation:

* lets study the graph and the inequality to solve the question

- the inequality y > -x - 2

∵ the form of the inequality is y > mx + c , m is the slope of the line

  and c is the y-intercept (the line intersect y-axis at point (0 , c)

∴ c = -2 that means the line intersect the y-axis at point (0 , -2)

∵ the sign of the inequality is >

∴ we shad the part over the line

  region a and b

- the inequality y < 2x + 1

∵ the form of the inequality is y > mx + c , m is the slope of the line

  and c is the y-intercept (the line intersect y-axis at point (0 , c)

∴ c = 1 that means the line intersect the y-axis at point (0 , 1)

∵ the sign of the inequality is <

∴ we shad the part under the line

  region b and c

∵ the common region between the two lines is region b

∴ region b will make the inequalities y < 2x + 1 and y > -x - 2 true

multiply length by height. multiply the length by the height, and then double the product. work out 10 x 10 results = 100 square inches, then work out 100 x 2 = 200. the answer is 200 square inches.

step-by-step explanation: