exam Maths Puzzle Numerical Ability

Find the domain of the function algebraically:
f(x) = (x^2+ 4)^1/2

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exam Other Question

Solve for x:
a) (4^x)(2^(x+3)=16(^2x-5)
b) (2x-1)(^1/2)=sqrt3
c) 8(^2x)+(8^x)-12=0
d) (x+3)(^2/3)=4 I hate to bother you (I have the answer to the question in the back of the book) but even though I know the answer, I do not understand HOW they came up with the answers.

Temple