Let f(x) = x2, x > 1, and g(x) = x.(a) Show that f(g(x)) = x, x > 1, and g(f(x)) = x,x >

QUESTION:

Let \(f(x)=x^{2}, x>1\) , and \(g(x)=\sqrt{x}\).

(a) Show that \(f(g(x))=x, x>1\) , and \(f(g(x))=x, x>1\)

(b) Show that \(f\) and \(g\) are not inverses by showing that the graphs of \(y=f(x)\) and \(y=g(x)\) are not reflections of one another about \( y=x\).

(c) Do parts (a) and (b) contradict one another? Explain.

Equation Transcription:

,

Text Transcription:

f(x)=x^2,x>1

g(x)=square root x

f(g(x))=x,x>1

g(f(x))=x, x>1

f

g

y=f(x)

y=g(x)

 y=x