Let f(x)=x^2 - 16. find f^-1(x).

Answers

Answer 1

Answer: $f(x)=x^2-16\n\ny=x^2-16\n\nx^2=y+16\n\nx=√(y+16)\n\nf^(-1)(x)=√(x+16)$

Answer 2

Answer: A quadratic function doesn't have inverse function. But you can find inverse function for each of its "arms".

$f(x)=x^2-16 \Rightarrow x_(vertex)=0\n y=x^2-16\n x^2=y+16\n x=-√(y+16) \vee x=√(y+16)\n f^(-1)(x)=-√(x+16) \hbox{ for } x<0\hbox{ (left arm)}\n f^(-1)(x)=√(x+16) \hbox{ for } x>0\hbox{ (right arm)}$

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Use the zero product property to find the solutions to the equation x2 – 9 = 16.

Answers

Answer: x=5 or x=−5

Step-by-step explanation:

A square has an area of 144 in2 is reduced by a factor of 1/6

Answers

Answer:

If a square has an area of 144 square inches and is reduced by a factor of 1/6, it means that both the length and width of the square are multiplied by the square root of 1/6.

To find the new side length, we can take the square root of 1/6 and multiply it by the original side length.

Original side length = sqrt(144) = 12 inches

New side length = (1/6)^(1/2) * 12 inches

Simplifying the calculation:

New side length = (1/√6) * 12 inches

Now we can calculate the new side length:

New side length ≈ 3.27 inches (rounded to two decimal places)

To find the new area, we square the new side length:

New area = (3.27 inches)^2 ≈ 10.68 square inches (rounded to two decimal places)

Therefore, after reducing the square by a factor of 1/6, the new side length is approximately 3.27 inches, and the new area is approximately 10.68 square inches.

Which angle is adjacent to ZCGD?
B
G
с
D
E

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Can you give more details please

Dan pays £714.73 a year in his car insurance. The insurance company reduces the price by 4.1%. How much does the insurance cost now? Give your answer to 2 DP.

Answers

Answer:

£682.57

Step-by-step explanation:

Dan pays £714.73 a year in his car insurance.

The price was reduced by 4.1%

To find the new cost of the insurance, we simply need to find 4.15% of £714.73 and then subtract that from the initial price of the insurance (£714.73)

4.5% of 714.73 is:

$(4.5)/(100) * 714.73$ = £32.16

Then, the cost of the insurance now is:

£714.73 - £32.16 = £682.57

The insurance now costs £682.57

Final answer:

To calculate the new price of the insurance, we first calculate the discount, which is 4.1% of the original price (£714.73). Then, subtract this discount from the original price. Understanding percentage reduction is fundamental in calculating such discounts.

Explanation:

To calculate the new cost of car insurance, we will subtract the 4.1% reduction from the original price of £714.73. The percentage reduction can be calculated using the formula: Discount = Original Price x (Percentage / 100).

In our case, the discount is given by: Discount = £714.73 x (4.1 / 100).

Then, we subtract this discount from the original price to obtain the new price of insurance: New Price = Original Price - Discount.

Insurance premiums are a significant factor in personal finance, but factors like discounts can make them more affordable. It is crucial to understand the concept of percentage reductions to comprehend how discounts significantly affect the final cost for services such as insurance.

Learn more about Percentage Reduction here:

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The length of a rectangle is 7m more than its width. The perimeter of the rectangle is 60m. What are the dimensions?