# Tutor profile: Grace C.

## Questions

### Subject: SAT II Mathematics Level 2

If 2^(x+1) = 8^(x-3), then x is ?

First, equalize both side of the base. 2^(x+1)=(2^3)^(x-3) Then, solve x 2^(x+1)=2^(3x-9) this means that (x+1) must equal to (3x-9) x+1=3x-9 10=2x 5=x The answer for this question is 5

### Subject: Mandarin

房間裡有一張灰色的書桌，一張藍色的床和一盞黃色的檯燈。 書桌上有兩本書，一本紅色，一本綠色。書桌的左邊有一張藍色的床，床上面有一隻紅色的熊。紅色的熊的後面是一盞黃色的檯燈。檯燈照亮整個房間。 Where is the bear? (a) behind the lamp (b) beneath the bed (c) on the desk (d) on the bed (e) on the lamp

(d) on the bed Translation: There is a grey desk, a blue bed, and a yellow lamp in the room. There are two books on the desk, one is red and one is green. On the left side of the desk, there is a blue bed. There is a red bear on the bed. Behind the bear is a yellow lamp. The lamp lights up the entire room.

### Subject: Pre-Calculus

Given f(x) = (x+4)/(x-5), which is the value of f^(-1)(x)?

f(x) inverse is the reciprocal of f(x), which means f^(-1)f(x)=x First, we need to make sure the formula is an one to one function. Then, set f(x)=y. Plug in y, therefore, the formula will be y=(x+4)/(x-5) The first step, calculate x=(-5y-4)/(1-y) -->in detail: y=(x+4)/(x-5) y*(x-5)=(x+4) xy-5y=x+4 xy-5y-4=x -5y-4=x-xy (-5y-4)=x*(1-y) (-5y-4)/(1-y)=x The second step, switch x and y : (-5x-4)/(1-x)=y The answer for this question is f^(-1)(x) = (-5x-4)/(1-x)

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