For the Functions $f ( x ) = \frac { 1 } { x - 2 }$

question 49

Essay

For the functions $f ( x ) = \frac { 1 } { x - 2 }$ and $g ( x ) = \frac { x } { x - 1 }$ , find $f + g$ , $f - g$ , $\mathrm { fg }$ , $\frac { f } { g }$ and their domains. Answer $f + g = \frac { 1 } { x - 2 } + \frac { x } { x - 1 } = \frac { x ^ { 2 } - x - 1 } { ( x - 2 ) ( x - 1 ) } \quad$ domain: $( - \infty , 1 ) \cup ( 1,2 ) \cup ( 2 , \infty )$
$$\begin{array} { l l } f - g = \frac { 1 } { x - 2 } - \frac { x } { x - 1 } = - \frac { x ^ { 2 } - 3 x + 1 } { ( x - 2 ) ( x - 1 ) } & \text { domain: } ( - \infty , 1 ) \cup ( 1,2 ) \cup ( 2 , \infty ) \\f g = \left( \frac { 1 } { x - 2 } \right) \left( \frac { x } { x - 1 } \right) = \frac { x } { ( x - 1 ) ( x - 2 ) } & \text { domain: } ( - \infty , 1 ) \cup ( 1,2 ) \cup ( 2 , \infty ) \\\frac { f } { g } = \frac { ( x - 1 ) } { ( x - 2 ) x } & \text { domain: } ( - \infty , 0 ) \cup ( 0,1 ) \cup ( 1,2 ) \cup ( 2 , \infty )\end{array}$$ 10.
Given $f ( x ) = 2 x - 2$ and $g ( x ) = 2 x ^ { 2 }$ , find $( g \circ f ) ( - 1 )$ .

Understand the distinctions between fluid and crystallized intelligence and how each evolves through adulthood.

Examine the concept of practical intelligence and its stability and application across the lifespan.

Explain the development and decline patterns of cognitive abilities, including abstract thinking and multitasking, in adulthood.

Understand the relationship between mean, standard deviation, and scores in a distribution.

---

Definitions:

Market Crashes

Market crashes represent dramatic declines in stock market values over a short period, often leading to widespread financial panic.

Market Bubbles

A phenomenon where the prices of assets in a particular market rise rapidly to levels far beyond their intrinsic values, often followed by a sharp decline.

Asian Market Crash

A significant and rapid decline in stock prices across major Asian stock markets.

Confirmation Bias

The predisposition towards identifying, understanding, prioritizing, and retaining info that supports and confirms preconceived notions or assumptions.