Find the domain and range ! 10 points math 3

The domain = (-∞ , -1/4) ∪ (-1/4 , ∞)

The range = (-∞ , 21/4)∪(21/4 , ∞)

The answer is not in the choices

Step-by-step explanation:

* Lets revise how to find the inverse function

- At first write the function as y = f(x)

- Then switch x and y

- Then solve for y

- The domain of f(x) will be the range of f^-1(x)

- The range of f(x) will be the domain of f^-1(x)

* Now lets solve the problem

- At first find the domain and the range of f(x)

∵ f(x) = (x - 9)/(21 - 4x)

- The domain is all real numbers except the value which

  makes the denominator = 0

- To find this value put the denominator = 0

∴ 21 - 4x = 0 ⇒ subtract 21 from both sides

∴ -4x = -21 ⇒ ÷ -4 both sides

∴ x = 21/4

∴ The domain = R - {21/4} OR the domain = (-∞ , 21/4)∪(21/4 , ∞)

* Now lets find the range

- The range will be all the values of real numbers except -1/4

 because the horizontal asymptote equation is y = -1/4

- To find the horizontal asymptote we find the equation y = a/b

 where a is the coefficient of x up and b is the coefficient of x down

∵ The coefficient of x up is 1 and down is -4

∴ The equation y = 1/-4

∴ The value of y = -1/4 does not exist

∴ The range = R - {-1/4} OR the range = (-∞ , -1/4) ∪ (-1/4 , ∞)

* Switch the domain and the range for the f^-1(x)

∴ The domain = (-∞ , -1/4) ∪ (-1/4 , ∞)

∴ The range = (-∞ , 21/4)∪(21/4 , ∞)

366

step-by-step explanation:

(1, –1), (16, –4), (36, –6)

step-by-step explanation:

given that the function is

this can also be written as

we have to graph this function and check which list of points lie on the graph

see attachment for graph:

we find that the points lying are (1,-1) (16,-4) and (36,-6)

since square root is there we find that x can only be posiitve but y can be since square root both positive and negative.