(x - 2)^2 will always be positive and will have a minimum value of 0
so f(x) will have minimum of 2
Range is [2,∞)
The function is (-x+3)/ (3x-2) and we get f(1)=1 and differentiation is f'(x)=-7/ (9x²- 12x+4).
Given that,
The function is (-x+3)/ (3x-2)
We have to find f(1) and f'(x).
Take the function expression
f(x)= (-x+3)/ (3x-2)
Taking x as 1 value
f(1)= (-1+3)/(3(1)-2)
f(1)=2/1
f(1)=1
Now, to get f'(x)
With regard to x, we must differentiate.
f(x) is in u/v
We know
u/v=(vu'-uv')/ v² (formula)
f'(x)= ((3x-2)(-1)- (-x+3)(3))/ (3x-2)²
f'(x)= ((-3x+2)-(-3x+9))/ 9x²- 12x+4
f'(x)=(-3x+2+3x-9)/ 9x²- 12x+4
f'(x)=2-9/ (9x²- 12x+4)
f'(x)=-7/ (9x²- 12x+4)
Therefore, The function is (-x+3)/ (3x-2) and we get f(1)=1 and differentiation is f'(x)=-7/ (9x²- 12x+4).
To learn more about function visit: brainly.com/question/14002287
#SPJ1
Answer:
z = 5
Step-by-step explanation:
Here, I am using the 30 60 90 right triangle rule
7+3 = 2x
z = 5
x = 5√3
<u>Given</u>:
Given that the triangle ABC is similar to triangle FGH.
We need to determine the value of x.
<u>Value of x:</u>
Since, the triangles are similar, then their sides are proportional.
Thus, we have;
Let us consider the proportion 
to determine the value of x.
Substituting AB = 9 cm, GF = 13.5 cm, BC = 15 cm and GH = x, we get;
Cross multiplying, we get;
Thus, the value of x is 22.5 cm
Hence, Option F is the correct answer.
There are a few possibilities:
- Indirect proof
- reductio ad absurdum
The second term refers to the idea of simplifying a claim down to an impossible absurd one.
