Question

College Algebra functions?

Answer 1

Answer:

See below.

Step-by-step explanation:

For the first one:

$f(x)=\frac{4x+3}{5x+2}$        

$f(\frac{1}{x})= \frac{4(\frac{1}{x})+3}{5(\frac{1}{x})+2 }$

First, multiply both top and bottom by $x$.

Thus:

$(\frac{4(\frac{1}{x})+3}{5(\frac{1}{x})+2 } )\cdot \frac{x}{x}$$=\frac{4+3x}{5+2x}$

It cannot be simplified further.

For the second one:

$g(x)=\sqrt{x^2-8x}$

$g(x-2)=\sqrt{(x-2)^2-8(x-2)}$

$\sqrt{(x^2-4x+4)-8x+16}$

$\sqrt{x^2-12x+20}$

And that cannot be simplified further.