Composite Functions

[disciple1912]

Decide whether the composite functions, f?g and g?f, are equal to x.

f(x)=x³+3, g(x)= ³?x-3

Note:x-3 is part of the ? i just couldn't extend it to fit it in, so please imagine it is.

 

[Mrspi]

Decide whether the composite functions, f?g and g?f, are equal to x.

f(x)=x³+3, g(x)= ³?x-3

Note:x-3 is part of the ? i just couldn't extend it to fit it in, so please imagine it is.

That's why God invented parentheses. If x - 3 is under the cube root sign, you can write it as

cuberoot(x - 3)........OR, you can write it as (x - 3)[sup:3ir05xj6](1/3)[/sup:3ir05xj6]

I'll help you with one part of this: f o g(x) would be
f(x) = x[sup:3ir05xj6]3[/sup:3ir05xj6] + 3, where you substitute (x - 3)[sup:3ir05xj6]1/3[/sup:3ir05xj6] for x

So,
f(g(x)) = ((x - 3)[sup:3ir05xj6](1/3)[/sup:3ir05xj6])[sup:3ir05xj6]3[/sup:3ir05xj6] + 3


f(g(x)) = (x - 3)[sup:3ir05xj6](1/3)*3[/sup:3ir05xj6] + 3

f(g(x)) = (x - 3)[sup:3ir05xj6]1[/sup:3ir05xj6] + 3

f(g(x)) = x - 3 + 3

f(g(x)) = x

There's half of your problem done.

Now, you do the same kind of thing to find g(f(x))