I need to pass this test

Mathematics

1 answer:

g100num [7]2 years ago

3 0

Answer:

C. f⁻¹(x) = 3 - 5x

Step-by-step explanation:

To find the inverse of a function, switch x and y and solve for y.

f(x) = (3 - x)/5

Change f(x) to y.

y = (3 - x)/5

Switch x and y.

x = (3 - y)/5

Multiply both sides by 5.

5x = 3 - y

Subtract 3 from both sides.

5x - 3 = -y

Multiply both sides by -1.

-5x + 3 = y

Switch the sides.

y = -5x + 3

Change the equation.

y = 3 - 5x

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Which of the following is an extraneous solution of (45-3x)^1/2=x-9?

Iteru [2.4K]

Answer:

C. x =3

Step-by-step explanation:

Extraneous solution is that root of a transformed equation that doesn't satisfy the equation in it's original form because it was excluded from the domain of the original equation.

Let's solve the equation first

$\sqrt{45-3x} = x-9\\Taking\ square\ on\ both\ sides\\{(\sqrt{45-3x})}^2 = {(x-9)}^2\\45-3x = x^2-18x+81\\0 = x^2-18x+81-45+3x\\x^2-15x+36 = 0\\x^2-12x-3x+36 = 0\\x(x-12)-3(x-12) = 0\\(x-3)(x-12)\\x-3 = 0\\=> x =3\\x-12 = 0\\x = 12\\We\ will\ check\ the\ solutions\ one\ by\ one\\So,\\for\ x=3\\\sqrt{45-3(3)} = 3-9\\\sqrt{45-9} = -6\\\sqrt{36}= -6\\6\neq -6\\For x=12\\\sqrt{45-3(12)} = 12-9\\\sqrt{45-36} = 6\\\sqrt{36}= 6\\6=6$