Given #f(x) = 3x - 2x#, #g(x) = sqrtx# and #h(x) = 3x^2 + 2# how do you find (g o f)(-2)?

1 Answer
Trevor Ryan.
Jan 6, 2016

If we work in the space of real numbers, then this is undefined, however if we work in the space of complex numbers, then the answer is #+-isqrt2#.

Explanation:

By definition, #(g@f)(x)=g[f(x)]#

#=g(3x-2x)#

#=g(x)#

#=sqrtx#.

#therefore (g@f)(-2)=g[f(-2)]=g(-2)=sqrt(-2)#

If we work in the space of real numbers, then this is undefined, however if we work in the space of complex numbers, then the answer is #+-isqrt2#.

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