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3 years ago

Does the equation y = x represent a function? Explain why or why not.

Mathematics

1 answer:

Sphinxa [80]3 years ago

3 0

Answer:

It represents a function because it consists of x-intercept and y-intercept hence can be plotted.

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Suppose h(x)=3x-2 and j(x) = ax +b. Find a relationship between a and b such that h(j(x)) = j(h(x))

sergejj [24]

Answer:

$\displaystyle a = \frac{1}{3} \text{ and } b = \frac{2}{3}$

Step-by-step explanation:

We can use the definition of inverse functions. Recall that if two functions, f and g are inverses, then:

$\displaystyle f(g(x)) = g(f(x)) = x$

So, we can let j be the inverse function of h.

Function h is given by:

$\displaystyle h(x) = y = 3x-2$

Find its inverse. Flip variables:

$x = 3y - 2$

Solve for y. Add:

$\displaystyle x + 2 = 3y$

Hence:

$\displaystyle h^{-1}(x) = j(x) = \frac{x+2}{3} = \frac{1}{3} x + \frac{2}{3}$

Therefore, a = 1/3 and b = 2/3.

We can verify our solution:

$\displaystyle \begin{aligned} h(j(x)) &= h\left( \frac{1}{3} x + \frac{2}{3}\right) \\ \\ &= 3\left(\frac{1}{3}x + \frac{2}{3}\right) -2 \\ \\ &= (x + 2) -2 \\ \\ &= x \end{aligned}$

And:

$\displaystyle \begin{aligned} j(h(x)) &= j\left(3x-2\right) \\ \\ &= \frac{1}{3}\left( 3x-2\right)+\frac{2}{3} \\ \\ &=\left( x- \frac{2}{3}\right) + \frac{2}{3} \\ \\ &= x \stackrel{\checkmark}{=} x\end{aligned}$

3 0

3 years ago

1 Example of linear absolute value equation & linear absolute value inequality

krek1111 [17]

Example:
Linear absolute value inequalities all have a similar equation of |ax + b| < c, except they can be less than, greater than, less than or equal to, or greater than or equal to.
Hope this helped :)

5 0

4 years ago

Twelve less than a number y is 8? Please help

evablogger [386]

Answer:

The answer is y = 20

Step-by-step explanation:

To find this, we need to turn it into an equation. Then we can follow the order of operations to solve.

y - 12 = 8

y = 20

7 0

3 years ago

Read 2 more answers

24. To what fraction is the arrow pointing to

sp2606 [1]

Image? where is it? id love to help

3 0

4 years ago

The question that follows this graph is:

azamat

Answer:

S'(5,-1), M'(1,-3)

Step-by-step explanation:

So, if the rotation is clockwise, the formula is (x,y)--->(-x,-y).

The original points are, (-1,3) and (-5,1).

Using the formula,

(-1,3) ----> (1,-3)

(-5,1) ----> (5,-1)

For the question in the image, the reflection over the x-axis is..

S'(-5,1) ---> (-5,-1)

M'(1,-3) ---> (-1,-3)

6 0

4 years ago