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3 years ago

The blue figure is a translation of the black image. Write a rule to describe the translation.

Mathematics

1 answer:

4vir4ik [10]3 years ago

5 0

it has gone up 4 lines and left -2 making it go for a (4,-2)

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The one-to-one functions g and h are defined as follows

Debora [2.8K]

Answer:

$g^-^1(x)=-8$

$h^-^1(x)=\frac{x-4}{3}$

$(h^-^1 \ o\ h)(-3)=-3$

Step-by-step explanation:

When given the following functions,

$g=[(-2,-7),(4,6),(6,-8),(7,4)]$

$h(x)=3x+4$

One is asked to find the following,

1. Question 1

$g^-^1(4)$

When finding the inverse of a function that is composed of defined points, one substitutes the input given into the function, then finds the output. After doing so, one must substitute the output into the function, and find its output. Thus, finding the inverse of the given input;

$g^-^1(4)$

$g(4)=6\\g(6)=-8\\g^-^1(4)=-8$

2. Question 2

$h^-^1(x)$

Finding the inverse of a continuous function is essentially finding the opposite of the function. An easy trick to do so is to treat the evaluator (h(x)) like another variable. Solve the equation for (x) in terms of (h(x)). Then rewrite the equation in inverse function notation,

$h(x)=3x+4\\\\h(x)-4=3x\\\\\frac{h(x)-4}{3}=x\\\\\frac{x-4}{3}=h^-^1(x)$

$h^-^1(x)=\frac{x-4}{3}$

3. Question 3

$(h^-^1 \ o\ h)(-3)$

This question essentially asks one to find the composition of the function. In essence, substitute function (h) into function ( $h^-^1$ ) and simplify. Then substitute (-3) into the result.

$h^-^1\ o\ h$

$\frac{(3x+4)-4}{3}\\\\=\frac{3x+4-4}{3}\\\\=\frac{3x}{3}\\\\=x$

Now substitute (-3) in place of (x),

$=-3$

8 0

3 years ago

If g(x)= x=2 and h(x) = 4 - X, what is the value of (gºh)(-3)?

navik [9.2K]

The required value of (g°h)(-3) is 5.

Step-by-step explanation:

Given,

g(x)= x-2 and h(x) = 4 - x

To find (g°h)(-3)

Now,

(g°h)(x) = g(h(x))

= g(4-x)

= (4-x)-2 = 2-x

So,

(g°h)(-3) = 2-(-3) = 5 [ putting x=-3]

8 0

3 years ago

Nicole has a board 88 in.long.she needs to to cut it into filt a space 80 3/8 in long

Aleks [24]

Cut 7 and 6/8 in
Vhcmcghm

6 0

3 years ago

What are they? I don’t quite understand it

Aleksandr [31]

The answers are:

Top Left - equilateral triangle (all three sides are equal)

Top Right - scalene triangle (no sides are equal)

Bottom Left - right angle triangle (one right angle)

Bottom Right - obtuse angle triangle ( one obtuse angle)

8 0

2 years ago

The length of a classroom is 35 feet. What is the measurement in YARDS and<br>FEET? *

notsponge [240]

Answer:

35 feet or 11 $\frac{2}{3}$ or ≈11.67 yards.

Step-by-step explanation:

A yard is 3 feet.

35÷3=

11.66... (6 continues forever) or 11 $\frac{2}3}$ (11 2/3) yards

7 0

3 years ago