Which of the following numbers is a square number? Check all that apply.

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

2 years ago

Helppppppp!!!!!!!!!!!!!!!!!!

charle [14.2K]

The two triangles that make up the parallelogram are congruent, which means their corresponding angles are congruent. The opposite angles are both 115 degrees and angle 1 is equal to 50 degrees, as they are corresponding angles.
Interior angles of triangles add to equal 180 degrees, so you can set up an equation to find m<2:

180 = 115 + 50 + x
180 = 165 + x
15 = x

Answer:
The measure of angle 2 is 15 degrees.

4 0

3 years ago

Enny White is shopping for CDs. She decides to purchase 3 movie soundtracks. The music store has 7 different movie soundtracks i

Gala2k [10]

Answer:

35 different selections of soundtracks are possible

Step-by-step explanation:

Total number of soundtracks available at the store = 7

Enny decides to purchase 3 movie soundtracks.

So, in this problem we have to find in how many ways can Enny chose 3 soundtracks out of 7. The order in which the soundtracks are chosen does not matter e.g soundtracks A,B and C are the same as soundtracks B,C and A.

In an arrangement when the order does not matter, we use combinations to find the total possible number of arrangements or selections.

So, for this problem choosing 3 soundtracks out of 7 means forming combinations from 7 objects taken 3 at a time. This can be represented mathematically as:

$^{7}C_{3}$