Friday, May 12, 2017

College Algebra, Chapter 3, 3.6, Section 3.6, Problem 36

Determine the functions fg,gf,ff and gg and their domains if f(x)=x3+2 and g(x)=3x
For fg

fg=f(g(x))Definition of fgfg=(3x)3+2Definition of gfg=x+2Definition of f

The domain of the function is (,)

For gf

gf=g(f(x))Definition of gfgf=3(x3+2)Definition of g

We know that if the index is an odd number then the domain of function is (,)

For ff

ff=f(f(x))Definition of ffff=(x3+2)3+2Definition of fff=x9+6x6+12x3+8+2Simplifyff=x9+6x6+12x3+10Definition of f

The domain of the function is (,)

For gg

gg=g(g(x))Definition of gggg=33xDefinition of ggg=6xDefinition of g

We know that if the index is any even number, the radicand can't have a negative value. So the domain of function is [0,)

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