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3 years ago

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What is the slope of the line x=5

1 answer:

Andre45 [30]3 years ago

5 0

The slope would go vertically starting it at 5. you place your dot at 5 and draw a line going up and down throughout both the top and bottom of the right side of the graph. hope it helped

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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

Write a rational expression in which x simplifies to x+3/x-10

tino4ka555 [31]

Answer:

Below.

Step-by-step explanation:

[(x - 3)(x +3)] / [(x - 3)(x - 10)]

The x-3 cancels out.

4 0

2 years ago

What is the equation to a graph with the vertex -1,3 and zeros -4 and -2

Mashutka [201]

Answer:

$f(x)=x^2+6x+8$

Step-by-step explanation:

We are given zeros as x=-4, x=-2

so, we can set up function as

$f(x)=a(x+4)(x+2)$

Vertex is at (-1,3)

It means that graph passes through point (-1,3)

so, we can plug x=-1 and f(x)=3

and then we can solve for 'a'

$3=a(-1+4)(-1+2)$

we get

$a=1$

now, we can plug it back

and we get

$f(x)=1(x+4)(x+2)$

now, we can simplify it

$f(x)=x^2+6x+8$

5 0

3 years ago

The first floor of a house consists of a kitchen, playroom, and dining room. The areas of the kitchen, playroom, and dining room

guapka [62]

Answer: don’t know give me brainless

Theory: cause

7 0

3 years ago

Find the prime factorization of 35.

jeka94

Answer:

1 5 7 35

Step-by-step explanation: im a differnet breed duh

7 0

2 years ago