Question

Given f(x) and g(x), write the function g(f(x)).

f(x)=x2−1;g(x)=x/1−x

Answer 1

What is g(x)? You have written \(g(x) = \dfrac{x}{1}-x\). Did you mean \(g(x) = \dfrac{x}{x-1}\)? If you meant the latter, then the parentheses are NOT optional: g(x) = x/(1-x)

Please write out g(1).
Please write out g(7).
Please write out g(p).
Please write out g(Chocolate).

Answer 2

g(x) is x/(x-1)

Answer 3

You need to see why the parentheses are mandatory.

Okay, now do the four assignments.

Answer 4

x/(x-1)(1)=x/(x-1)
when i put the second one in my calculator i get x/(x-1)(7)=-6.5
g(p)??
and g(Chocolate)??

Answer 5

When you find your initial function of f(g(x)), you will get this:\[g(x)=(\frac{ x }{ x-1})^{2}-1\]

Answer 6

That's the thing, there are no variables to plug in...

Answer 7

And what you put isn't one of the options...

Answer 8

i see that...I thought @tkhunny's reply was the values you needed to plug in like it was part of the problem. But it's not. So what I posted there is your solution.

Answer 9

hmmm then...

Answer 10

To find g(f(x)), you take your f function and fill in every x you see with the g function.

Answer 11

If \[f(x)=x ^{2}-1\]you replace the x with \[\frac{ x }{x-1 }\]. Doing that gives you\[g(f(x))=(\frac{ x }{ x-1 })^{2}-1\]This is not the wrong answer for what you have typed for your functions so I cannot figure out why there is a discrepancy.

Answer 12

my options are

a. \[x^2-1/(1-(x^2))\]

b. \[1-x^2/(1+x^2)\]

c. \[1-x^2/(2+x^2)\]

d. \[x^2-1/(2-x^2)\]

Answer 13

f(x)=x2−1;g(x)=x/1−x
\(f(x)=x^2-1\) \(\color{blue}{g(x)=\frac{x}{1-x}}\)
f(g(x)) means you start with f(x) and insert g(x) where you see x
\[f(x)=x^2-1 \rightarrow \color{blue}{\left( \frac{x}{1-x} \right)^2}-1\]
you then need to simplify

Answer 14

so would it be option b? \[1-x^2/1+x^2\]

Answer 15

It was practice. There are no numbers to solve this one.

f(x)=x2−1;g(x)=x/(1−x)

\(g(f(x)) = \dfrac{f(x)}{1-f(x)} = \dfrac{x^{2} - 1}{1 - (x^{2} - 1)} = \dfrac{x^{2} - 1}{2-x^{2}}\)

The correct option is not presented. Perhaps you have not copied things correctly and made a few more parentheses errors.