0.9 how far will he travels if the wheels on his unicycle completes 1,000 rotation

Consider the functionf:R→Rdefined viaf(x) =|x|.(a) Give a functiongwith domainRsuch thatg◦fis one-to-one, or describe why it is

yaroslaw [1]

Answer:

(a) Is not possible

(b) It is possible

(c) It is possible

(d) Is NOT possible.

Step-by-step explanation:

(a)

Is not possible, notice that for any function $g$ such that

$g : \mathbb{R} \rightarrow \mathbb{R}$

you would have that

$(g\circ f)(x) = g(f(x)) = g(|x|)$

And for, lets say -3,3 you have that

$g(|-3|) = g(|3|) = g(3)$ therefore is not possible to find a function that is one to one.

(b)

It is possible. Take the following function

$g(x) = x\sin(x)$ since $\sin$ is periodic it will take positive and negative numbers and if you multiply by $x$ each period will become bigger and bigger.

(c)

It is possible. Take the function

$g(x) = \sqrt{x}$

Then

$(f \circ g )(x) = | \sqrt{x} | = \sqrt{x}$ and $\sqrt{x}$ is one to one.

(d)

It is NOT possible because $(f\circ g)(x) = f(g(x)) = |g(x)|$ and that will always be positive.

7 0

3 years ago

Solve for a: a/2 - 2/3 = a + 1/5

ki77a [65]

The answer is 4 if I am correct

3 0

3 years ago

Read 2 more answers

Given the quadratic equation (x + p)²=49,where p is a constant,find the values of p if one of the roots of the equation is 4.

blondinia [14]

Answer:

-11, 3

Step-by-step explanation:

We know one of the roots are

$(x+ 4) {}^{2} = 49$

$x + 4 = - 7$

$x + 4 = 7$

$x = - 11$

or

$x = 3$

7 0

3 years ago

Find an equation of the line that is parallel to the graph of 2x+3y=5 and contains the point (3, −1).

uranmaximum [27]

Answer:

A) Equation of line is 3X - 2Y = 11

B) Equation of line is Y = X + 1

C) Equation of line is Y - 7 = 0

Equation of line , point (3 , -1) and slop $\frac{3}{2}$ is 3X - 2Y = 11

Step-by-step explanation:

Given equation of line as 2x + 3y = 5

slove of this line (m1) = - $\frac{2}{3}$

Now another line passes through point (3 , -1) having slop (m2)

Both lines are parallel to each other, i.e (m1) × (m2) = - 1

So slop of second line (m2 ) = $\frac{-1}{m1}$

(m2) = $\frac{-1}{(\frac{-2}{3} } )$

(m2) = $\frac{3}{2}$

Now eq of line with point (3 , -1) and slop (m2)

Y- y1 = (m2)( X - x1)

Or, Y +1 = $\frac{3}{2}$ (X - 3)

i.e 2Y + 2= 3X - 9

∴ Equation of line is 3X - 2Y = 11 Answer

B) Given points as ( 5,6) and (3 , 4)

Slop (m) = $\frac{y2 - y1}{x2 - x1}$ = $\frac{4 - 6}{3 - 5}$ = 1

So the equation of line is

Y- y1 = (m)( X - x1)

Y - 6 = (1) (X - 5)

i.e Equation of line is Y = X + 1 Answer

C) Given points as ( 0, 7) , (0 , -8)

Slop (m) with co-ordianate = $\frac{y2 - y1}{x2 - x1}$

Or, = $\frac{-8 - 7}{0 - 0}$

=0

Hence equation of line is Y - 7 = 0 Answer

7 0

3 years ago

Write a rational expression that is equal to the following rational expression when x does not equal 1 or -5

SpyIntel [72]

4x+20 is your answer here

3 0

3 years ago