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Sergio039 [100]

4 years ago

9

What’s the answer to this question?

1 answer:

NemiM [27]4 years ago

4 0

Answer:

y=1/2x

Step-by-step explanation:

The slope of the line goes up by 1 over by 2 each time or 1/2. (Rise over run)

This can be proven by substituting X and Y for a point on the graph.

y=5, x=10

5=1/2(10)

5=5

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

goblinko [34]

Answer:

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

Step-by-step explanation:

<u>Definition of the inverse of a function</u>

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 $\sqrt{x}\:+\:4$

5 0

1 year ago

3/4-1/2 can u please explain how to do this

katen-ka-za [31]

1/4
first find lcm=4
second corporate it inti the fraction 1/2=2/4
third, subtract
3/4-2/4=1/4

6 0

4 years ago

Mischa wrote the quadratic equation 0 = –x2 + 4x – 7 in standard form. What is the value of c in her equation

Zolol [24]

Mischa wrote the quadratic equation 0 = –x2 + 4x – 7 in standard form

The standard form of quadratic equation is

$y= ax^2 + bx + c$

When y=0 then the standard equation becomes

$0= ax^2 + bx + c$

Now we compare the given equation $0 = -x^2 + 4x - 7$ with $0= ax^2 + bx + c$ and find the value of a, b,c

-x^2 can be written as -1x^2

$0= ax^2 + bx + c$

$0 = -1x^2 + 4x - 7$

a= -1 , b=4 and c=-7

The value of c is -7

4 0

4 years ago

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Dee whether the bangles are shofe, welte a similarity<br> statement<br> AV<br> X

AleksandrR [38]

Answer:

Step-by-step explanation:

ı do not know

3 0

3 years ago

Johnny ate 200 jars of his fathers sugar if johnny got a warning from his papa (While T-posing and floating to him) every 10 jar

katen-ka-za [31]

Answer:

I assume the answer would be that f(x) = 6(x) increases over the interval x = 3 to x = 4

Step-by-step explanation:6 x 3 is 18 and 6 x 4 is 24, so over the interval x = 3 to x = 4 f(x) would increase.

7 0

3 years ago

Read 2 more answers