im confuse with math??

Question

help with these problems please teach me how to do

1) List all real values ofx such that f(x)=o. If there are no such real x, type DNE in the answer blank. If there is more that one real x, give a comma separated list (i.e.: 1,2).

f(x)=12+17/x-4

2)Evaluate the function f(x)=8x^2-8x+10 at the indicated values

f(x^2)=?

3) find the Domain of -3x^2-15x+12

Answer 1

1) Do you mean f(x)=0? (o is not the same as 0)
f(x) = 12+17/x-4
Is that 12 + 17/(x - 4), or 12 + (17/x) - 4? (again they're not the same)

I'll assume it's 12 + 17/(x - 4).
To find the values of x for which f(x) = 0 means to find the values of x for which 12 + 17/(x - 4) = 0.

Using standard algebra, you can subtract 12 from both sides of the equation:
17/(x - 4) = -12
Then you multiply both sides by (x - 4):
17 = -12(x - 4)
Then you divide both sides by -12:
17/(-12) = x - 4
You can write this more easily as:
x - 4 = -17/12
Add 4 to both sides:
x = 4 - 17/12 = 48/12 - 17/12 = 31/12.


2) f(x)=8x^2-8x+10
What are the indicated values? Substitute each value you are given for x. So and do the arithmetic. For example, if you were asked the value 2, you substitute x = 2:
8 (2^2) - 8 (2) + 10 = 8*4 - 8*2 + 10 = 26.

f(x^2) means you substitute x^2 for x. In other words, whereever you see x in the original, you put x^2 in the answer:
f(x^2) = 8(x^2)^2 + 8(x^2) + 10.
Since (x^2)^2 = x^(2*2) = x^4, the answer is:
f(x^2) = 8x^4 + 8x^2 + 10.

3) the domain is the set of values of x for which you can work out the value of a function of x. You can work out the value of -3x^2-15x+12 for all real numbers, so the domain is all real numbers.

Answer 2

f(x)=12+17/x-4 = 0
when 8 + 17/x =0
17/x = -8
x = - 17/8

f(x)=8x^2-8x+10
f(u)=8u^2-8u+10
Put u =x^2
f(x^2)= 8(x^2)^2 - 8(x^2) + 10
= 8x^4 - 8x^2 + 10


find the Domain of y = -3x^2-15x+12
it is defined on all x from -inifinit to + infinity

To find the range of y (extra)
it has a max when dy/dx = 0
dy/dx = -6x - 15 = 0
x = -15/6 = -5/2
when ymax = -3 (5/2)^2 - 15(-5/2) + 12
= -75/4 + 75/2 + 12
= 12 + 75/4
= 12 + 18.75 = 30.75

and it can take any lower values of y

so range of y is from -infinity to 30.75

Answer 3

1)
f(x)=12+17/x-4
0 = 12+17/x-4
-17/x-4 = 12
12(x - 4) = -17
12x - 48 = -17
12x = 48 - 17
12x = 31
x = 31/12

2)
f(x)=8x^2-8x+10
f(x^2) = 8(x^2)^2 - 8x^2 + 10
f(x^2) = 8x^4 - 8x^2 + 10

3)
-3x^2-15x+12 > 0
Domain = all real numbers

Answer 4

1.
0 = 12 + 17/(x-4)
-12 = 17/(x-4)
-12(x-4) = 17
-12x + 48 = 17
-12x = -31
x = 31/12

2. ?

3. The domain is all real numbers.

Answer 5

12+17/x-4=0
12(x-4)+17=0
12x-48+17=0
12x=31
x=31/12

2)f(x^2)=8(x^2)^2-8(x^2)+10=8x^4-8x^2+10

3) the domain=R

Answer 6

1) 12+17/(x-4)=0
x-4=-17/12
x=31/12