Question

Composition of Functions and Inverses: Question 6Which expression represents the composite function f(g(x)) iff(x) = 2x - 1 and g(x) = 1/x-1? A. 2x-1/x-1B.3-x/x-1C.1/2(x+1)D.1/2(x-1)

Answer 1

ANSWER

$\text{ f}(g(x))\text{ = }\frac{3\text{ - x}}{x\text{ - 1}}$

EXPLANATION

We want to find the composite function f(g(x)).

To do this, we simply replace x in f(x) with the g(x) function.

We have that:

$\begin{gathered} f(x)\text{ = 2x - 1} \\ \text{and} \\ g(x)\text{ = }\frac{1}{x\text{ - 1}} \end{gathered}$

Therefore:

$\begin{gathered} f(g(x))\text{ = 2(}\frac{1}{x\text{ - 1}}\text{) - 1} \\ f(g(x))\text{ = }\frac{2}{x\text{ - 1}}\text{ - 1} \\ f(g(x))\text{ = }\frac{2\text{ - (x - 1)}}{x\text{ - 1}}\text{ = }\frac{2\text{ - x + 1}}{x\text{ - 1}} \\ \Rightarrow\text{ f}(g(x))\text{ = }\frac{3\text{ - x}}{x\text{ - 1}} \end{gathered}$