(fog)(x) and (gof)(x)

[kjones]

Consider the functins f(x) = the square root of x + 3

and

g(x) = x^2 - 3.

a) (fog) (x)


b) (gof) (x)


c) (f+g) (x)


d) (fg) (x)


I know the rules for combing the functions:


Can somebody help check behind me on c) and d) and show me a) and b)?

Thanks again. K

 

[daon]

\(\displaystyle f(x) = \sqrt{x+3}\\ g(x) = x^2-3\)



a) (fog) (x)
\(\displaystyle f(g(x)) = \sqrt{g(x)+ 3} = \sqrt{x^2-3+3} = |x|\)


b) (gof) (x)
\(\displaystyle g(f(x)) = (\sqrt{x+3})^2 - 3 = ...\)


c) (f+g) (x)
\(\displaystyle f(x) + g(x) = ...\)


d) (fg) (x)
\(\displaystyle f(x) \times g(x) = ...\)

 

[kjones]

For:

a) (fog) (x) = 400.07 ?

b) (gof) (x) = 400 ?

c) (f = g) (x) = 400.500 ? ?

d) (fg) (x) = 693.107 ? ? ?

Correct?

K

 

[daon]

For:

a) (fog) (x) = 400.07 ?

b) (gof) (x) = 400 ?

c) (f = g) (x) = 400.500 ? ?

d) (fg) (x) = 693.107 ? ? ?

Correct?

K

How can we check if you haven't given us an x value?