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3 years ago

I am confusion. help me

Mathematics

1 answer:

timofeeve [1]3 years ago

6 0

Multiple the two Collins

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I NEED HELP WITH QUESTION PLEASE!! What is the inverse of f(x) (x) = (x-4)² for x ≥ 4?

goblinko [34]

Answer:

4th choice $\bold{f^{-1}(x) = \sqrt{x} + 4}$

Step-by-step explanation:

Definition of the inverse of a function

A function g is the inverse of a function f if whenever y=f(x) then x=g(y). In other words, applying f and then g is the same thing as doing nothing. We can write this in terms of the composition of f and g as g(f(x))=x. The domain of f becomes the range of g and the range of f becomes the domain of g

To solve for the inverse of the function $f(x) =\left(x-4\right)^2$

Let $y=\left(x-4\right)^2$

$\mathrm{Replace}\:x\:\mathrm{with}\:y$ $\text{ and replace }\:y\:\mathrm{with}\:x$

$x=\left(y-4\right)^2$

Switch sides
$\left(y-4\right)^2=x$

Take square roots on both sides
$y-4=\pm\sqrt{x}$

Add 4 on both sides to solve for y

$y = \pm\sqrt{x} + 4$

We have two solutions

$y=\sqrt{x}+4,\:y=-\sqrt{x}+4$

To determine which one of these to be chosen not that in the given choices we can eliminate the first two since x cannot be negative

The third choice can also be eliminated since
$-\sqrt{x} + 4$ is a decreasing function for $x \ge 0$

So the last answer choice is correct and the inverse of $f(x) = (x-4)^2$

is given by $f^{-1}(x) = \sqrt{x} + 4$

Answer:4th choice $\bold{f^{-1}(x) = \sqrt{x} + 4}$

Note

Domain of (x-4)² is [4, ∞) since x ≥ 4 and (x-4)² cannot be negative

Range of (x-4)² is [0, ∞)

Domain of $\sqrt{x}\:+\:4$ is [0, ∞)

Range of $\sqrt{x}\:+\:4$ is [4, ∞)

so indeed the domain of (x-4)² has become the range of $\sqrt{x}\:+\:4$ and the range of (x-4)² has become the domain of $\sqrt{x}\:+\:4$

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1 year ago

trisha started out with 40,000 miles on her car and drove exactly 800 miles a week. After how many weeks did she have 44,800 mil

Yuri [45]

Since she started out with 40,000 miles, you have to subtract that from 44,800 miles. you end up with 4,800 miles. you then divide 4,800 miles by 800 miles and you end up with 6 as your answer.

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3 years ago

Question Help Find the original price of a pair of shoes if the sale price is $11 after a 75% discount.

fenix001 [56]

If it was a 75% discount, then u r actually paying 25%

so....25% of the original price is $ 11

0.25x = 11
x = 11 / 0.25
x = 44 <=== the original price

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3 years ago

Point P is located at (−2, 7), and point R is located at (1, 0). Find the y value for the point Q that is located two thirds the

Sladkaya [172]

7 + (0-7) * 2/3 = 7 - 14/3 = (21 - 14) / 3 = 7/3 = 2.3

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3 years ago

Y’all plz- help this is so hard giving brainlest ;)

stiv31 [10]

Answer:

Step-by-step explanation: