Functions

[F19]

For the function:

f(x)= sqrt(x+1) / (5 - x)

*the (x+1) is in a square root divided by (5-x)


Find:

f(f(x))

This is really urgent, any help is appreciated.

Thanks.

 

[Denis]

sqrt(x+1) / (5 - x)
*the (x+1) is in a square root divided by (5-x)

That was well posted...

Can you square this: sqrt(x+1) / (5 - x) ?

 

[mmm4444bot]

… This is really urgent…

Why?



If you have a textbook, look for "functions; composition" or "composition of functions" in the index.

f(x) is function notation. The variable x represents the expression that we "input" into function f. The symbolism f(x) represents the expression that comes "out" of function f.

If you have f(2), then the input is 2; you substitute 2 for x everywhere x appears in the definition for f.

If you have f(x + 1), then the input is the expression x + 1; you substitute x + 1 for x everywhere it appears.

If you have f[f(x)], then you substitute the expression for f(x) for x because f(x) is being used as an input into itself.

Here's an example.

g(x) = sin(x)/(x^2 + 1)

g[g(x)] is what we get by substituting the expression sin(x)/(x^2 + 1) for x everywhere x appears in the expression sin(x)/(x^2 + 1)

\(\displaystyle \frac{\sin\left(\frac{sin(x)}{x^2 \;+\; 1}\right)}{\left(\frac{sin(x)}{x^2 \;+\; 1}\right)^2 \;+\; 1}\)

That's what function composition looks like when we input a function into itself.

Can you try to substitute the expression sqrt(x + 1)/(5 - x) for x everywhere x appears in the same expression [i.e., the definition of f(x)] ?

Please show your work.