## Question 10: Let the function y=f(x) be continuous on (mathbb{R}) and have a graph of the function (y=f'(x)) as shown below. On what interval is the function (g(x)=f(1-x)+frac{x^{2}}{2}-x) inverse?

Question 10: Let the function y=f(x) be continuous on (mathbb{R}) and have a graph of the function (y=f'(x)) as shown below. On what interval is the function (g(x)=f(1-x)+frac{x^{2}}{2}-x) inverse? A. (((1 ; 3)) B. ((-thirty first)) C. (left(-1 ; frac{3}{2}right)) D. ((-2 ; 0)) (begin{array}{l} g^{prime}(x)=-f^{prime}(1-x)+x-1, forall mathrm{x} in mathbb{R } \ g^{prime}(x)=-f^{prime}(1-x)+x-1 leq 0 …

## Question 9: Given the function (f( x)=ax^{5}+bx^{4}+cx^{3}+dx^{2}+c x+f quad( a, b, c, d, c, f in mathbb{R})). Know that the graph of a function has a graph like the one shown below. Ask the function (g( x)=f (1-2 x)-2 x^{2}+1) covariate on which of the following intervals?

Question 9: Given the function (f( x)=ax^{5}+bx^{4}+cx^{3}+dx^{2}+c x+f quad( a, b, c, d, c, f in mathbb{R})). Know that the graph of a function has a graph like the one shown below. Ask the function (g( x)=f (1-2 x)-2 x^{2}+1) covariate on which of the following intervals? A. (left(-frac{3}{2} ;-1right)) B. ((-ten)) C. (((1;3)) D. …

## Question 8: Given the function y=f(x) The function (y=f'(x)) has a graph as shown below. How many integer values ​​(m in .)[-10 ; 10]) so that the function (g(x)=f( 1-2 x+m)+x^{2}-(m+1) x+m^{2}) is inverse on the interval (1 ; 2 )

Question 8: Given the function y=f(x) The function (y=f'(x)) has a graph as shown below. How many integer values ​​(m in .)[-10 ; 10]) so that the function (g(x)=f( 1-2 x+m)+x^{2}-(m+1) x+m^{2}) is inverse on the interval (1 ; 2 ) A. 1 B. 2 C. 3 D. 4 (begin{array}{l} g^{prime}(x)=-2 f^{prime}(1-2 x+m)+2 xm-1, forall …

## Question 7: Given the function f(x). The graph y=f'(x) is given as shown below. The function (g(x)=f(x-1)-frac{x^{2}}{2}) is inverse in which of the following ranges?

Question 7: Given the function f(x). The graph y=f'(x) is given as shown below. The function (g(x)=f(x-1)-frac{x^{2}}{2}) is inverse in which of the following ranges? A. (1 ; 3) B. (-2 ; 1) C. (2 ; 4) D. (0 ; 1) (begin{array}{l} text { We have: } g(x)=f(x-1)-frac{x^{2}}{2} Rightarrow g^{prime}( x)=f^{prime}(x-1)-x \ Rightarrow g^{prime}(x)=0 Leftrightarrow …

## Question 6: Given the function y=f(x). The function y = f'(x) has a graph as shown below. The function (g(x)=fleft(x^{2}+2 xright)-x^{2}-2 x) is covariate on which of the following intervals?

Question 6: Given the function y=f(x). The function y = f'(x) has a graph as shown below. The function (g(x)=fleft(x^{2}+2 xright)-x^{2}-2 x) is covariate on which of the following intervals? A. ((-1-sqrt{2} ;-1)) B. ((-1-sqrt{2} ;-1+sqrt{2})) C. ((-1 ;-1+sqrt{2})) D. ((-1 ;+infty)) (begin{array}{l} text { We have: } g(x)=fleft(x^{2}+2 xright)-x^{2}-2 x \ Rightarrow g^{prime}(x)=(2 x+2) …

## A24 will stream The Green Knight for one night on August 18th

A24’s The Green Knight will make its virtual debut much earlier than expected — on August 18th, you’ll be able to buy a \$20 ticket to stream the film through A24’s Screening Room platform. The one-night-only stream isn’t a full streaming release for rental or purchase, given that The Green Knight is still otherwise exclusive …

## Nvidia’s tiny RTX A2000 GPU can fit inside a small form factor PC

Nvidia is launching its new RTX A2000 GPU today, designed for professional workstations. It’s Nvidia’s smallest Ampere-based GPU so far and can easily squeeze into small form factor workstations. Like Nvidia’s old Quadro cards, the RTX A2000 is designed primarily for professionals who want to leverage ray tracing and Nvidia’s AI capabilities, and it’s the …

## CyberDog is a new ominous-looking robot from Xiaomi

Chinese tech giant Xiaomi has unveiled a quadrupedal robot named CyberDog: an experimental, open-source machine that the firm says “holds unforetold possibilities.” CyberDog is the latest example of tech companies embracing the quadrupedal form factor in robotics. The most notable example of the trend is Spot, a machine built by US firm Boston Dynamics. Spot …

## Google One VPN expands internationally to Canada, Mexico, UK, and more

Google is expanding the VPN service that it provides as part of its Google One subscription to seven new countries: Mexico, Canada, the United Kingdom, France, Germany, Spain, and Italy, as spotted by 9to5Google. The company started offering VPN access to 2TB Google One cloud storage subscribers in the US late last year, as a …

## Xiaomi announces Mix 4 with under-display camera

Xiaomi has announced the Mix 4, the first phone in the Mi Mix series to be announced in nearly three years. The Mix phones have always been about bezel-less designs with seamless screens, and the Mix 4 carries on that idea by commercializing a technology that Xiaomi has been working on for a long time: …