Function f and g(x)

[alyren]

1)For the given functions f and g, find the requested function and state its domain.

f(x)= sqrt(x+11); g(x)=2/x

Find f.g

so far i solved as [sqrt(x+11)/1] x (2/x) = [(2sqrt(x+11)/(x)], domain is all real except 0. i don't know if i was right, it seem to be wrong.

2) how to graph a function using the techniques of shifting, compressing, stretching, and/or reflecting
f(x) = -3(x+1)^2-3

 

[mmm4444bot]

[sqrt(x+11)/1] x (2/x) Do you "see" any issue, typing three variables, in this expression ?

When we start algebra, we stop using x as a multiplication sign. Use an asterisk or implied multiplication, instead.

sqrt(x + 11) * 2/x = 2 sqrt(x + 11)/x

[sqrt(x + 11)](2/x) = 2 sqrt(x + 11)/x

[(2sqrt(x+11)/(x)], domain is all real except 0. Try evaluating f*g at x = -12.

You should then realize the error in your domain.

By the way, you're missing a close parenthesis, above.

Actually, the expression is clear without most of those grouping symbols:

2 sqrt(x + 11)/x

how to graph a function using the techniques of shifting, compressing, stretching, and/or reflecting

f(x) = -3(x + 1)^2 - 3

Here's the progression.

x^2 : parabola

(x + 1)^2 : horizontally shifted 1 unit leftward

-(x + 1)^2 : reflected across the x-axis

-3(x + 1)^2 : vertically stretched by a factor of 3

-3(x + 1)^2 - 3 : vertically shifted 3 units downward

 

[alyren]

Thank you mmm4444bot for all your help, i will try my best on how to posting equation. i am new to online tying equations.

 

[mmm4444bot]

THIS SITE provides the basic conventions, for typing math using a keyboard.