Can you help me find this ans

Prove that the function

Stella [2.4K]

Answer:

See proof below

Step-by-step explanation:

Important points

understanding what it means to be "onto"
the nature of a quadratic function
finding a value that isn't in the range

Onto

For a function with a given co-domain to be "onto," every element of the co-domain must be an element of the range.

However, the co-domain here is suggested to be $\mathbb R$ , whereas the range of f is not $\mathbb R$ (proof below).

Proof (contradiction)

Suppose that f is onto $\mathbb R$ .

Consider the output 7 (a specific element of $\mathbb R$ ).

Since f is onto $\mathbb R$ , there must exist some input from the domain $\mathbb R$ , "p", such that f(p) = 7.

Substitute and solve to find values for "p".

$f(x)=-3x^2+4\\f(p)=-3(p)^2+4\\7=-3p^2+4\\3=-3p^2\\-1=p^2$

Next, apply the square root property:

$\pm \sqrt{-1} =\sqrt{p^2}$

By definition, $\sqrt{-1} =i$ , so

$i=p \text{ or } -i =p$

By the Fundamental Theorem of Algebra, any polynomial of degree n with complex coefficients, has exactly n complex roots. Since the degree of f is 2, there are exactly 2 roots, and we've found them both, so we've found all of them.

However, neither $i$ nor $-i$ are in $\mathbb R$ , so there are zero values of p in $\mathbb R$ for which f(p)= 7, which is a contradiction.

Therefore, the contradiction supposition must be false, proving that f is not onto $\mathbb R$

3 0

2 years ago

7

LUCKY_DIMON [66]

The answer is B. 15 cm

5 0

3 years ago

When I get multiplied by any number, the sum of the figures in the product is always me. What am I?

vladimir1956 [14]

Answer: 9

Step-by-step explanation:

When you multiply 9*9, you get 81 whose sum is 9 (8+1)

Likewise, 9*8=72( 7+2=9)

8 0

3 years ago

Read 2 more answers

Find the equation of the lines parallel and perpendicular to the line 5x+2y=12 through the point (-2,3)

muminat

Answer:

The equation of line parallel to given line and passing through points ( - 2 , 3 ) is 5 x + 2 y + 4 = 0

The equation of line perpendicular to given line and passing through points ( - 2 , 3 ) is 2 x - 5 y + 19 = 0

Step-by-step explanation:

Given equation of line as :

5 x + 2 y = 12

or, 2 y = - 5 x + 12

or , y = $\frac{-5}{2}$ x + $\frac{12}{2}$

Or, y = $\frac{-5}{2}$ x + 6

∵ Standard equation of line is give as

y = m x + c

Where m is the slope of line and c is the y-intercept

Now, comparing given line equation with standard eq

So, The slope of the given line = m = $\frac{-5}{2}$

Again,

The other line if passing through the points (- 2 , 3 ) And is parallel to given line

So, for parallel lines condition , the slope of both lines are equal

Let The slope of other line = M

So, M = m = $\frac{-5}{2}$

∴ The equation of line with slope M and passing through points ( -2 , 3) is

y = M x + c

Now , satisfying the points

So, 3 = $\frac{-5}{2}$ × ( - 2 ) + c

or, 3 = $\frac{10}{2}$ + c

Or, 3 = 5 + c

∴ c = 3 - 5 = - 2

c = - 2

So, The equation of line with slope $\frac{-5}{2}$ and passing through points ( -2 , 3)

y = $\frac{-5}{2}$ x - 2

or, 2 y = - 5 x - 4

I.e 5 x + 2 y + 4 = 0

Similarly

The other line if passing through the points (- 2 , 3 ) And is perpendicular to given line

So, for perpendicular lines condition,the products of slope of both lines = - 1

Let The slope of other line = M'

So, M' × m = - 1

Or, M' × $\frac{-5}{2}$ = - 1

Or, M' = $\frac{-1}{\frac{-5}{2}}$

Or, M' = $\frac{2}{5}$

∴ The equation of line with slope M and passing through points ( -2 , 3) is

y = M' x + c'

Now , satisfying the points

So, 3 = $\frac{2}{5}$ × ( - 2 ) + c'

or, 3 = $\frac{- 4}{5}$ + c'

Or, 3 × 5 = - 4 + 5× c'

∴ 5 c' = 15 + 4

or, 5 c' = 19

Or, c' = $\frac{19}{5}$

So, The equation of line with slope $\frac{2}{5}$ and passing through points ( -2 , 3)

y = $\frac{2}{5}$ x + $\frac{19}{5}$

y = $\frac{2 x + 19}{5}$

Or, 5 y = 2 x + 19

Or, 2 x - 5 y + 19 = 0

Hence The equation of line parallel to given line and passing through points ( - 2 , 3 ) is 5 x + 2 y + 4 = 0

And The equation of line perpendicular to given line and passing through points ( - 2 , 3 ) is 2 x - 5 y + 19 = 0

Answer

4 0

3 years ago

I have 25% off coupon that I would like to apply to this purchase.” Since the sticker price is $93.78,the actual cost to you wil

levacccp [35]

Answer:

$70.33

Step-by-step explanation:

sticker price = $93.78

discount coupon in percentage = 25%

Thus, discount will be 25% of sticker price

discount amount = 25% of $93.78 = 25/100 * $93.78 = $23.45

Thus, amount paid = sticker price - discount amount = $93.78-$23.45

amount paid = $70.33

actual cost to you will be what after discount applied is $70.33

4 0

4 years ago

Can you help me find this ans​

Can you help me find this ans