MaxWong

1.\(\quad (f\cdot g)(x)\\=(x^2-7x+12)(\dfrac{7}{x^2}-16)\\ = 7 - \dfrac{49}{x}+\dfrac{84}{x^2}-16x^2+112x-192\\ =-16x^2+112x-185-\dfrac{49}{x}+\dfrac{84}{x^2}\)

2.\(f(x)=\sqrt{2x}-6\\ y=\sqrt{2x}-6\\ x = \sqrt{2y}-6\\ \sqrt{2y}=x+6\\ 2y = x^2 + 12x + 36\\ y = \dfrac{x^2}{2}+6x+18\\ f^{-1}(x)=\dfrac{x^2}{2}+6x+18\)

Really? It doesn't work for me!

\(\begin{array}{rll}4x^2+15&=&x^2+18x\\3x^2-18x+15&=&0\\x^2-6x+5&=&0\\(x-1)(x-5)&=&0\end{array}\\\text{Either one of the factors equal 0.}\\\begin{array}{rl}x-1=0&x-5=0\\x=1&x=5\\\end{array}\)

\(\dfrac{a}{b}\times c = \dfrac{a\times c }{b}\).

Examples: 

\(\dfrac{5}{7} \times 2 = \dfrac{5\times 2}{7}= \dfrac{10}{7}=1\dfrac{3}{7}\)

\(\dfrac{2}{3}\times 15 = \dfrac{30}{3}=10\)

\(\dfrac{4}{9}\times 32 = \dfrac{128}{9} = 14\dfrac{2}{9}\)

22521008071930811247210364724710555878336746262578603045969925706618268298469415658031134405487.2423412144568778 according to the calculator. Just copy and paste.

The usual CPhill does this:

6 + 20/2 - 1

= 6 + 10 - 1

= 16 - 1

= 15.

And you gave a wrong answer, imposter.

I am in 9th grade in your educational system and I am actually a Secondary 3 student.(That doesn't mean 3rd grade, strange)

It is just all about distributive property of multiplication.

Distributive property of multiplication: \(a \times (b + c) = a \times b + a \times c\)

Example:

23 x 45

= (20 + 3) x (40 + 5)

= 40 x (20 + 3) + 5 x (20 + 3) <--- Distributive property of multiplication

= 40 x 20 + 40 x 3 + 5 x 20 + 5 x 3 <-- again Distributive property of multiplication

So that we do this when we are told to find the product with partial products.

In our country we use 23 x 40 + 23 x 5 though.

\(\begin{array}{rll}&2&3\\\times&4&5\\-&-&-\\20&\times&40=800\\3&\times&40=120\\20&\times&5\;\;=100\\3&\times&5\quad \!\!\!=15\\--&-&-----\end{array}\)

800 + 120 + 100 + 15 = 900 + 135 = 1035.

Check with this calculator: 23 x 45 = 1035

Tips: Use * for multiplication on this calculator!! :)