All categories

3 years ago

If f(x-3)=x^2-4x+5, what's f(1-x)

Mathematics

1 answer:

olganol [36]3 years ago

4 0

Answer:

$\large\boxed{f(1-x)=x^2-4x+5}$

Step-by-step explanation:

$f(x-3)=x^2-4x+5\\\\f((x-3)+3)\to\text{put x + 3 to the equation of the function:}\\\\f(x-3+3)=(x+3)^2-4(x+3)+5\\\text{use the distributive property and}\ (a+b)^2=a^2+2ab+b^2\\f(x)=x^2+2(x)(3)+3^2+(-4)(x)+(-4)(3)+5\\f(x)=x^2+6x+9-4x-12+5\qquad\text{combine like terms}\\f(x)=x^2+(6x-4x)+(9-12+5)\\f(x)=x^2+2x+2\\\\f(1-x)\to\text{put 1 - x to the equation of the funtion f(x):}\\\\f(1-x)=(1-x)^2+2(1-x)+2\\\text{use the distributive property and}\ (a-b)^2=a^2-2ab+b^2$

$f(1-x)=1^2-2(1)(x)+x^2+(2)(1)+(2)(-x)+2\\f(1-x)=1-2x+x^2+2-2x+2\qquad\text{combine like terms}\\f(1-x)=x^2+(-2x-2x)+(1+2+2)\\f(1-x)=x^2-4x+5$

You might be interested in

The length of each side of an equilateral triangle is increased by 20%, resulting in triangle ABC. If the length of each side of

kompoz [17]

Answer: Area of ΔABC is 2.25x the area of ΔDEF.

Step-by-step explanation: Because equilateral triangle has 3 equal sides, area is calculated as

$A=\frac{\sqrt{3} }{4} a^{2}$

with a as side of the triangle.

Triangle ABC is 20% bigger than the original, which means its side (a₁) measures, compared to the original:

a₁ = 1.2a

Then, its area is

$A_{1}=\frac{\sqrt{3} }{4}(1.2a)^{2}$

$A_{1}=\frac{\sqrt{3} }{4}1.44a^{2}$

Triangle DEF is 20% smaller than the original, which means its side is:

a₂ = 0.8a

So, area is

$A_{2}=\frac{\sqrt{3} }{4} (0.8a)^{2}$

$A_{2}=\frac{\sqrt{3} }{4} 0.64a^{2}$

Now, comparing areas:

$\frac{A_{1}}{A_{2}}= (\frac{\sqrt{3}.1.44a^{2} }{4})(\frac{4}{\sqrt{3}.0.64a^{2} } )$

$\frac{A_{1}}{A_{2}} =$ 2.25

The area of ΔABC is 2.25x greater than the area of ΔDEF.

7 0

2 years ago

The speed limit is 25 miles per hour, but it seems that many of the cars are going faster. The city places 2 counter strips 360

klio [65]

You figure out how long it would take a car traveling at 25 mph
to cover 360 ft. Any driver who does it in less time is speeding.

   (25 mi/hr) · (5,280 ft/mile) · (1 hr / 3,600 sec)

   = (25 · 5280 / 3600) ft/sec = (36 and 2/3) feet per second.

To cover 360 ft at 25 mph, it would take

360 ft / (36 and 2/3 ft/sec) = 9.82 seconds .

Anybody who covers the 360 feet in less than 9.82 seconds
is moving faster than 25 mph.
_________________________________

If you're interested, here's how to do it in the other direction:

Let's say a car covers the 360 feet in ' S ' seconds.
What's the speed of the car ?

   (360 ft / S sec) · (1 mile / 5280 feet) · (3600 sec/hour)

   = (360 · 3600) / (S · 5280) mile/hour

   = 245.5 / S miles per hour .

The teacher timed one car crossing both strips in 7.0 seconds.
How fast was that car traveling ?

   245.5 / 7.0 = 35.1 miles per hour

Another teacher timed another car that took 9.82 seconds to cross
both strips. How fast was this car traveling ?

245.5 / 9.82 = 25 miles per hour

7 0

2 years ago

What is the value of h? Oh = 20 Oh = 35 40° 0 h = 55 0 h = 70 (2h) (2h)

Levart [38]

Answer:

I think its 55

Step-by-step explanation:

3 0

3 years ago

Read 2 more answers

A company has $54,000 in a bank account that pays an interest of 2% per year. How much money can I withdraw at the end of one ye

RSB [31]

Answer:

$55,080

Step-by-step explanation:

Hope this helps.

3 0

2 years ago

Read 2 more answers

Need help on this please Help. I would really appreciate it :)

Ierofanga [76]

Answer:

i am not sure but according to me ans is d

Step-by-step explanation:

Ax+By=C

Ax=C-By

A=C-By/x

5 0

2 years ago

If f(x-3)=x^2-4x+5, what's f(1-x)​

If f(x-3)=x^2-4x+5, what's f(1-x)